181-530: A stellarator confines plasma using external magnets. Scientists aim to use stellarators to generate fusion power . It is one of many types of magnetic confinement fusion devices, most commonly tokamak . The name "stellarator" refers to stars because fusion mostly occurs in stars such as the Sun . It is one of the earliest human-designed fusion power devices. The stellarator was invented by American scientist Lyman Spitzer in 1951. Much of its early development
362-400: A 7-dimensional phase space . When used in combination with a high Hall parameter , a critical value triggers the problematic electrothermal instability which limited these technological developments. Although the underlying equations governing plasmas are relatively simple, plasma behaviour is extraordinarily varied and subtle: the emergence of unexpected behaviour from a simple model is
543-659: A Neutrality Pact in April 1941, and Japan adopted the doctrine of Nanshin-ron , promoted by the Navy, which took its focus southward and eventually led to war with the United States and the Western Allies. In Europe, Germany and Italy were becoming more aggressive. In March 1938, Germany annexed Austria , again provoking little response from other European powers. Encouraged, Hitler began pressing German claims on
724-443: A Penning trap and positron plasmas. A dusty plasma contains tiny charged particles of dust (typically found in space). The dust particles acquire high charges and interact with each other. A plasma that contains larger particles is called grain plasma. Under laboratory conditions, dusty plasmas are also called complex plasmas . For plasma to exist, ionization is necessary. The term "plasma density" by itself usually refers to
905-578: A cautious French probe into the Saarland . The Western Allies also began a naval blockade of Germany , which aimed to damage the country's economy and war effort. Germany responded by ordering U-boat warfare against Allied merchant and warships, which would later escalate into the Battle of the Atlantic . On 8 September, German troops reached the suburbs of Warsaw . The Polish counter-offensive to
1086-548: A charged plasma particle affects and is affected by the fields created by the other charges. In turn, this governs collective behaviour with many degrees of variation. Plasma is distinct from the other states of matter. In particular, describing a low-density plasma as merely an "ionized gas" is wrong and misleading, even though it is similar to the gas phase in that both assume no definite shape or volume. The following table summarizes some principal differences: Three factors define an ideal plasma: The strength and range of
1267-406: A divertor , which removed impurities from the plasma, greatly reducing the x-ray cooling effect seen on earlier machines. B-64 included straight sections in the curved ends which gave it a squared-off appearance. This appearance led to its name, it was a "figure-8, squared", or 8 squared, or 64. This led to experiments in 1956 where the machine was re-assembled without the twist in the tubes, allowing
1448-405: A q around 1 ⁄ 3 , while experiments on tokamaks demonstrated it needs to be at least 1. Machines following this rule showed dramatically improved performance. However, by the mid-1980s the easy path to fusion disappeared; as the amount of current in the new machines began to increase, a new set of instabilities in the plasma appeared. These could be addressed, but only by greatly increasing
1629-480: A C model, which would attempt to actually create fusion reactions at a large scale. This entire series was expected to take about a decade. Around the same time, Jim Tuck had been introduced to the pinch concept while working at Clarendon Laboratory at Oxford University . He was offered a job in the US and eventually ended up at Los Alamos, where he acquainted the other researchers with the concept. When he heard Spitzer
1810-638: A Munich-based spin-off from the Max Planck Institute for Plasma Physics, which steered the W7-X experiment. Heating a gas increases the energy of the particles within it, so by heating a gas into hundreds of millions of degrees, the majority of the particles within it reach the energy required to fuse. According to the Maxwell–Boltzmann distribution , some of the particles will reach the required energies at much lower average temperatures. Because
1991-418: A bulk temperature of about 50 million Celsius, still very hot but within the range of existing experimental systems. The key problem was confining such a plasma; no material container could withstand those temperatures. But because plasmas are electrically conductive, they are subject to electric and magnetic fields which provide a number of solutions. In a magnetic field, the electrons and nuclei of
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#17327829084882172-403: A certain number of neutral particles may also be present, in which case plasma is called partially ionized . Neon signs and lightning are examples of partially ionized plasmas. Unlike the phase transitions between the other three states of matter, the transition to plasma is not well defined and is a matter of interpretation and context. Whether a given degree of ionization suffices to call
2353-533: A few examples given in the following table: Plasmas are by far the most common phase of ordinary matter in the universe, both by mass and by volume. Above the Earth's surface, the ionosphere is a plasma, and the magnetosphere contains plasma. Within our Solar System, interplanetary space is filled with the plasma expelled via the solar wind , extending from the Sun's surface out to the heliopause . Furthermore, all
2534-415: A gas-like state of matter known as plasma . According to the ideal gas law , like any hot gas, plasma has an internal pressure and thus wants to expand. For a fusion reactor, the challenge is to keep the plasma contained. In a magnetic field, the electrons and nuclei orbit around the magnetic field lines, confining them to the area defined by the field. A simple confinement system can be made by placing
2715-457: A means to calculate the electric field from the density: E → = k B T e e ∇ n e n e . {\displaystyle {\vec {E}}={\frac {k_{\text{B}}T_{e}}{e}}{\frac {\nabla n_{e}}{n_{e}}}.} It is possible to produce a plasma that is not quasineutral. An electron beam, for example, has only negative charges. The density of
2896-644: A much greater emphasis on the theoretical understanding of the plasma. In 1961, Melvin B. Gottlieb took over the Matterhorn Project from Spitzer, and on 1 February the project was renamed as the Princeton Plasma Physics Laboratory (PPPL). Continual modification and experimentation on the Model C slowly improved its operation, and the confinement times eventually increased to match that of Bohm predictions. New versions of
3077-503: A neutral gas or subjecting it to a strong electromagnetic field . The presence of charged particles makes plasma electrically conductive , with the dynamics of individual particles and macroscopic plasma motion governed by collective electromagnetic fields and very sensitive to externally applied fields. The response of plasma to electromagnetic fields is used in many modern devices and technologies, such as plasma televisions or plasma etching . Depending on temperature and density,
3258-629: A new department for all of these projects, becoming "Project Sherwood". With the funding from the AEC, Spitzer began work by inviting James Van Allen to join the group and set up an experimental program. Allen suggested starting with a small "tabletop" device. This led to the Model A design, which began construction in 1952. It was made from 5-centimetre (2.0 in) pyrex tubes about 350 cm (11.5 ft) in total length, and magnets capable of about 1,000 gauss. The machine began operations in early 1953 and clearly demonstrated improved confinement over
3439-405: A non-neutral plasma must generally be very low, or it must be very small, otherwise, it will be dissipated by the repulsive electrostatic force . The existence of charged particles causes the plasma to generate, and be affected by, magnetic fields . Plasma with a magnetic field strong enough to influence the motion of the charged particles is said to be magnetized. A common quantitative criterion
3620-412: A plasma. One is based on representing the smoothed distribution function on a grid in velocity and position. The other, known as the particle-in-cell (PIC) technique, includes kinetic information by following the trajectories of a large number of individual particles. Kinetic models are generally more computationally intensive than fluid models. The Vlasov equation may be used to describe the dynamics of
3801-524: A pretext to initiate the invasion. The first German attack of the war came against the Polish defences at Westerplatte . The United Kingdom responded with an ultimatum for Germany to cease military operations, and on 3 September, after the ultimatum was ignored, Britain and France declared war on Germany. During the Phoney War period, the alliance provided no direct military support to Poland, outside of
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#17327829084883982-781: A pretext to worsen relations. On 29 August, Hitler demanded that a Polish plenipotentiary immediately travel to Berlin to negotiate the handover of Danzig , and to allow a plebiscite in the Polish Corridor in which the German minority would vote on secession. The Poles refused to comply with the German demands, and on the night of 30–31 August in a confrontational meeting with the British ambassador Nevile Henderson , Ribbentrop declared that Germany considered its claims rejected. On 1 September 1939, Germany invaded Poland after having staged several false flag border incidents as
4163-524: A problem that came to be known as " pump out ". This effect was causing plasma drift rates that were not only higher than classical theory suggested but also much higher than the Bohm rates. B-3's drift rate was a full three times that of the worst-case Bohm predictions, and failed to maintain confinement for more than a few tens of microseconds. As early as 1954, as research continued on the B-series machines,
4344-409: A second heating system known as magnetic pumping. This machine was also modified to add an ultra-high vacuum system. Unfortunately, B-2 demonstrated little heating from the magnetic pumping, which was not entirely unexpected because this mechanism required longer confinement times, and this was not being achieved. As it appeared that little could be learned from this system in its current form, in 1958 it
4525-475: A secret protocol that defined German and Soviet "spheres of influence" (western Poland and Lithuania for Germany; eastern Poland , Finland, Estonia , Latvia and Bessarabia for the Soviet Union), and raised the question of continuing Polish independence. The pact neutralised the possibility of Soviet opposition to a campaign against Poland and assured that Germany would not have to face the prospect of
4706-408: A secret research lab at Princeton University that would carry on theoretical work on H-bombs after he returned to the university in 1951. Spitzer was invited to join this program, given his previous research in interstellar plasmas. But by the time of his trip to Aspen, Spitzer had lost interest in bomb design, and upon his return, he turned his attention full-time to fusion as a power source. Over
4887-774: A similar pact and rejected ceding part of its territory to the Soviet Union. The Soviet Union invaded Finland in November 1939, and was subsequently expelled from the League of Nations for this crime of aggression. Despite overwhelming numerical superiority, Soviet military success during the Winter War was modest, and the Finno-Soviet war ended in March 1940 with some Finnish concessions of territory . In June 1940,
5068-594: A substance "plasma" depends on the specific phenomenon being considered. Plasma was first identified in laboratory by Sir William Crookes . Crookes presented a lecture on what he called "radiant matter" to the British Association for the Advancement of Science , in Sheffield, on Friday, 22 August 1879. Systematic studies of plasma began with the research of Irving Langmuir and his colleagues in
5249-429: A system of charged particles interacting with an electromagnetic field. In magnetized plasmas, a gyrokinetic approach can substantially reduce the computational expense of a fully kinetic simulation. Plasmas are studied by the vast academic field of plasma science or plasma physics , including several sub-disciplines such as space plasma physics . Plasmas can appear in nature in various forms and locations, with
5430-415: A temperature of about a billion kelvins . Due to the Maxwell–Boltzmann statistics , a bulk gas at a much lower temperature will still contain some particles at these much higher energies. Because the fusion reactions release so much energy, even a small number of these reactions can release enough energy to keep the gas at the required temperature. In 1944, Enrico Fermi demonstrated that this would occur at
5611-531: A toroidal tube. The configuration is characterized by a 'rotational transform', such that a single line of magnetic force, followed around the system, intersects a cross-sectional plane in points which successively rotate about the magnetic axis. ... A rotational transform may be generated either by a solenoidal field in a twisted, or figure-eight shaped, tube, or by the use of an additional transverse multipolar helical field, with helical symmetry. While working at Los Alamos in 1950, John Wheeler suggested setting up
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5792-418: A tube inside the open core of a solenoid . The tube can be evacuated and then filled with the requisite gas and heated until it becomes a plasma. The plasma naturally wants to expand outwards to the walls of the tube, as well as move along it, towards the ends. The solenoid creates magnetic field lines running down the center of the tube, and the plasma particles orbit these lines, preventing their motion towards
5973-531: A two-front war, as it had in World War I. Immediately afterwards, Hitler ordered the attack to proceed on 26 August, but upon hearing that the United Kingdom had concluded a formal mutual assistance pact with Poland and that Italy would maintain neutrality, he decided to delay it. In response to British requests for direct negotiations to avoid war, Germany made demands on Poland, which served as
6154-495: A typical feature of a complex system . Such systems lie in some sense on the boundary between ordered and disordered behaviour and cannot typically be described either by simple, smooth, mathematical functions, or by pure randomness. The spontaneous formation of interesting spatial features on a wide range of length scales is one manifestation of plasma complexity. The features are interesting, for example, because they are very sharp, spatially intermittent (the distance between features
6335-408: Is applied across a dielectric gas or fluid (an electrically non-conducting material) as can be seen in the adjacent image, which shows a discharge tube as a simple example ( DC used for simplicity). The potential difference and subsequent electric field pull the bound electrons (negative) toward the anode (positive electrode) while the cathode (negative electrode) pulls the nucleus. As
6516-417: Is close to a Maxwellian even in the presence of strong electric or magnetic fields. However, because of the large difference in mass between electrons and ions, their temperatures may be different, sometimes significantly so. This is especially common in weakly ionized technological plasmas, where the ions are often near the ambient temperature while electrons reach thousands of kelvin. The opposite case
6697-507: Is much larger than the features themselves), or have a fractal form. Many of these features were first studied in the laboratory, and have subsequently been recognized throughout the universe. Examples of complexity and complex structures in plasmas include: Striations or string-like structures are seen in many plasmas, like the plasma ball , the aurora , lightning , electric arcs , solar flares , and supernova remnants . They are sometimes associated with larger current densities, and
6878-632: Is not affected by Debye shielding . To completely describe the state of a plasma, all of the particle locations and velocities that describe the electromagnetic field in the plasma region would need to be written down. However, it is generally not practical or necessary to keep track of all the particles in a plasma. Therefore, plasma physicists commonly use less detailed descriptions, of which there are two main types: Fluid models describe plasmas in terms of smoothed quantities, like density and averaged velocity around each position (see Plasma parameters ). One simple fluid model, magnetohydrodynamics , treats
7059-480: Is one of four fundamental states of matter (the other three being solid , liquid , and gas ) characterized by the presence of a significant portion of charged particles in any combination of ions or electrons . It is the most abundant form of ordinary matter in the universe , mostly in stars (including the Sun ), but also dominating the rarefied intracluster medium and intergalactic medium . Plasma can be artificially generated, for example, by heating
7240-409: Is that a particle on average completes at least one gyration around the magnetic-field line before making a collision, i.e., ν c e / ν c o l l > 1 {\displaystyle \nu _{\mathrm {ce} }/\nu _{\mathrm {coll} }>1} , where ν c e {\displaystyle \nu _{\mathrm {ce} }}
7421-436: Is the z-pinch plasma where the ion temperature may exceed that of electrons. Since plasmas are very good electrical conductors , electric potentials play an important role. The average potential in the space between charged particles, independent of how it can be measured, is called the "plasma potential", or the "space potential". If an electrode is inserted into a plasma, its potential will generally lie considerably below
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7602-426: Is the average ion charge (in units of the elementary charge ). Plasma temperature, commonly measured in kelvin or electronvolts , is a measure of the thermal kinetic energy per particle. High temperatures are usually needed to sustain ionization, which is a defining feature of a plasma. The degree of plasma ionization is determined by the electron temperature relative to the ionization energy (and more weakly by
7783-475: Is the electron gyrofrequency and ν c o l l {\displaystyle \nu _{\mathrm {coll} }} is the electron collision rate. It is often the case that the electrons are magnetized while the ions are not. Magnetized plasmas are anisotropic , meaning that their properties in the direction parallel to the magnetic field are different from those perpendicular to it. While electric fields in plasmas are usually small due to
7964-606: Is the ion density and n n {\displaystyle n_{n}} the neutral density (in number of particles per unit volume). In the case of fully ionized matter, α = 1 {\displaystyle \alpha =1} . Because of the quasineutrality of plasma, the electron and ion densities are related by n e = ⟨ Z i ⟩ n i {\displaystyle n_{e}=\langle Z_{i}\rangle n_{i}} , where ⟨ Z i ⟩ {\displaystyle \langle Z_{i}\rangle }
8145-604: The Anglo-German Naval Agreement and the German–Polish declaration of non-aggression . The situation became a crisis in late August as German troops continued to mobilise against the Polish border. On 23 August the Soviet Union signed a non-aggression pact with Germany, after tripartite negotiations for a military alliance between France, the United Kingdom, and Soviet Union had stalled. This pact had
8326-689: The British Empire , with fighting in the Balkans , Mediterranean, and Middle East , the aerial Battle of Britain and the Blitz , and naval Battle of the Atlantic . Through a series of campaigns and treaties, Germany took control of much of continental Europe and formed the Axis alliance with Italy , Japan , and other countries. In June 1941, Germany led the European Axis in an invasion of
8507-581: The German Revolution of 1918–1919 , and a democratic government, later known as the Weimar Republic , was created. The interwar period saw strife between supporters of the new republic and hardline opponents on both the political right and left. Italy, as an Entente ally, had made some post-war territorial gains; however, Italian nationalists were angered that the promises made by the United Kingdom and France to secure Italian entrance into
8688-853: The German invasion of Poland and the United Kingdom and France 's declaration of war on Germany two days later on 3 September 1939. Dates for the beginning of the Pacific War include the start of the Second Sino-Japanese War on 7 July 1937, or the earlier Japanese invasion of Manchuria , on 19 September 1931. Others follow the British historian A. J. P. Taylor , who stated that the Sino-Japanese War and war in Europe and its colonies occurred simultaneously, and
8869-576: The Italian mainland , and Allied offensives in the Pacific—cost the Axis powers their initiative and forced them into strategic retreat on all fronts. In 1944, the Western Allies invaded German-occupied France at Normandy , while the Soviet Union regained its territorial losses and pushed Germany and its allies westward. At the same time, Japan suffered reversals in mainland Asia, while the Allies crippled
9050-553: The Japanese Navy and captured key islands . The war in Europe concluded with the liberation of German-occupied territories ; the invasion of Germany by the Western Allies and the Soviet Union, culminating in the fall of Berlin to Soviet troops; Hitler's suicide ; and the German unconditional surrender on 8 May 1945 . Following the refusal of Japan to surrender on the terms of the Potsdam Declaration ,
9231-695: The League of Nations as a force to preserve peace. Both Italy and Ethiopia were member nations, but the League did little when the former clearly violated Article X of the League's Covenant . The United Kingdom and France supported imposing sanctions on Italy for the invasion, but the sanctions were not fully enforced and failed to end the Italian invasion. Italy subsequently dropped its objections to Germany's goal of absorbing Austria . When civil war broke out in Spain, Hitler and Mussolini lent military support to
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#17327829084889412-731: The Nationalist rebels , led by General Francisco Franco . Italy supported the Nationalists to a greater extent than the Nazis: Mussolini sent more than 70,000 ground troops, 6,000 aviation personnel, and 720 aircraft to Spain. The Soviet Union supported the existing government of the Spanish Republic . More than 30,000 foreign volunteers, known as the International Brigades , also fought against
9593-690: The Rome–Berlin Axis . A month later, Germany and Japan signed the Anti-Comintern Pact , which Italy joined the following year. The Kuomintang (KMT) party in China launched a unification campaign against regional warlords and nominally unified China in the mid-1920s, but was soon embroiled in a civil war against its former Chinese Communist Party (CCP) allies and new regional warlords . In 1931, an increasingly militaristic Empire of Japan , which had long sought influence in China as
9774-619: The Second World War (1 September 1939 – 2 September 1945) was a global conflict between two coalitions: the Allies and the Axis powers . Nearly all the world's countries —including all the great powers —participated, with many investing all available economic, industrial, and scientific capabilities in pursuit of total war , blurring the distinction between military and civilian resources. Tanks and aircraft played major roles , with
9955-590: The Soviet–Japanese Neutrality Pact in April 1941. By contrast, the Germans were steadily making preparations for an attack on the Soviet Union, massing forces on the Soviet border. Hitler believed that the United Kingdom's refusal to end the war was based on the hope that the United States and the Soviet Union would enter the war against Germany sooner or later. On 31 July 1940, Hitler decided that
10136-598: The Stresa Front in April 1935 in order to contain Germany, a key step towards military globalisation ; however, that June, the United Kingdom made an independent naval agreement with Germany, easing prior restrictions. The Soviet Union, concerned by Germany's goals of capturing vast areas of Eastern Europe , drafted a treaty of mutual assistance with France. Before taking effect, though, the Franco-Soviet pact
10317-709: The Sudetenland , an area of Czechoslovakia with a predominantly ethnic German population. Soon the United Kingdom and France followed the appeasement policy of British Prime Minister Neville Chamberlain and conceded this territory to Germany in the Munich Agreement , which was made against the wishes of the Czechoslovak government, in exchange for a promise of no further territorial demands. Soon afterwards, Germany and Italy forced Czechoslovakia to cede additional territory to Hungary, and Poland annexed
10498-707: The Tanggu Truce was signed in 1933. Thereafter, Chinese volunteer forces continued the resistance to Japanese aggression in Manchuria , and Chahar and Suiyuan . After the 1936 Xi'an Incident , the Kuomintang and CCP forces agreed on a ceasefire to present a united front to oppose Japan. The Second Italo-Ethiopian War was a brief colonial war that began in October 1935 and ended in May 1936. The war began with
10679-579: The Trans-Olza region of Czechoslovakia. Although all of Germany's stated demands had been satisfied by the agreement, privately Hitler was furious that British interference had prevented him from seizing all of Czechoslovakia in one operation. In subsequent speeches Hitler attacked British and Jewish "war-mongers" and in January 1939 secretly ordered a major build-up of the German navy to challenge British naval supremacy. In March 1939, Germany invaded
10860-558: The Treaty of Craiova . The loss of one-third of Romania's 1939 territory caused a coup against King Carol II, turning Romania into a fascist dictatorship under Marshal Ion Antonescu , with a course set towards the Axis in the hopes of a German guarantee. Meanwhile, German-Soviet political relations and economic co-operation gradually stalled, and both states began preparations for war. In April 1940, Germany invaded Denmark and Norway to protect shipments of iron ore from Sweden , which
11041-749: The United Kingdom and France to declare war on Germany. Poland was divided between Germany and the Soviet Union under the Molotov–Ribbentrop Pact , in which they had agreed on " spheres of influence " in Eastern Europe. In 1940, the Soviets annexed the Baltic states and parts of Finland and Romania . After the fall of France in June 1940, the war continued mainly between Germany and
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#173278290848811222-521: The United States Atomic Energy Commission (AEC) for funding to develop the system. He outlined a plan involving three stages. The first would see the construction of a Model A, whose purpose was to demonstrate that a plasma could be created and that its confinement time was better than a torus . If the A model was successful, the B model would attempt to heat the plasma to fusion temperatures. This would be followed by
11403-709: The Wehrmacht rapidly advanced to the Channel and cut off the Allied forces in Belgium, trapping the bulk of the Allied armies in a cauldron on the Franco-Belgian border near Lille. The United Kingdom was able to evacuate a significant number of Allied troops from the continent by early June, although they had to abandon almost all their equipment. On 10 June, Italy invaded France , declaring war on both France and
11584-451: The aftermath of World War I and the rise of fascism in Europe and militarism in Japan . Key events leading up to the war included Japan's invasion of Manchuria , the Spanish Civil War , the outbreak of the Second Sino-Japanese War , and Germany's annexations of Austria and the Sudetenland . World War II is generally considered to have begun on 1 September 1939, when Nazi Germany , under Adolf Hitler , invaded Poland , prompting
11765-404: The reunification of East and West Germany to take place and resolved most post–World War II issues. No formal peace treaty between Japan and the Soviet Union was ever signed, although the state of war between the two countries was terminated by the Soviet–Japanese Joint Declaration of 1956 , which also restored full diplomatic relations between them. World War I had radically altered
11946-480: The voltage increases, the current stresses the material (by electric polarization ) beyond its dielectric limit (termed strength) into a stage of electrical breakdown , marked by an electric spark , where the material transforms from being an insulator into a conductor (as it becomes increasingly ionized ). The underlying process is the Townsend avalanche , where collisions between electrons and neutral gas atoms create more ions and electrons (as can be seen in
12127-460: The 1920s, recall that Langmuir first used the term by analogy with the blood plasma . Mott-Smith recalls, in particular, that the transport of electrons from thermionic filaments reminded Langmuir of "the way blood plasma carries red and white corpuscles and germs." Plasma is called the fourth state of matter after solid , liquid , and gas . It is a state of matter in which an ionized substance becomes highly electrically conductive to
12308-479: The 1920s. Langmuir also introduced the term "plasma" as a description of ionized gas in 1928: Except near the electrodes, where there are sheaths containing very few electrons, the ionized gas contains ions and electrons in about equal numbers so that the resultant space charge is very small. We shall use the name plasma to describe this region containing balanced charges of ions and electrons. Lewi Tonks and Harold Mott-Smith, both of whom worked with Langmuir in
12489-409: The Allies were attempting to cut off . Denmark capitulated after six hours , and despite Allied support , Norway was conquered within two months. British discontent over the Norwegian campaign led to the resignation of Prime Minister Neville Chamberlain , who was replaced by Winston Churchill on 10 May 1940. On the same day, Germany launched an offensive against France . To circumvent
12670-400: The Axis war against the Soviet Union, in Romania's case partially to recapture territory ceded to the Soviet Union . In early June 1940, the Italian Regia Aeronautica attacked and besieged Malta , a British possession. From late summer to early autumn, Italy conquered British Somaliland and made an incursion into British-held Egypt . In October, Italy attacked Greece , but the attack
12851-470: The B-1 was that during the heating process, the particles would remain confined for only a few tenths of a millisecond, while once the field was turned off, any remaining particles were confined for as long as 10 milliseconds. This appeared to be due to "cooperative effects" within the plasma. Meanwhile, a second machine known as B-2 was being built. This was similar to the B-1 machine but used pulsed power to allow it to reach higher magnetic energy and included
13032-452: The B-1, which used ohmic heating (see below) to reach plasma temperatures around 100,000 degrees. This machine demonstrated that impurities in the plasma caused large x-ray emissions that rapidly cooled the plasma. In 1956, B-1 was rebuilt with an ultra-high vacuum system to reduce the impurities but found that even at smaller quantities they were still a serious problem. Another effect noticed in
13213-481: The Blitz , but largely ended in May 1941 after failing to significantly disrupt the British war effort. Using newly captured French ports, the German Navy enjoyed success against an over-extended Royal Navy , using U-boats against British shipping in the Atlantic . The British Home Fleet scored a significant victory on 27 May 1941 by sinking the German battleship Bismarck . In November 1939,
13394-668: The Chilean border. Known as the Huemul Project , this was completed in 1951. Richter soon convinced himself fusion had been achieved in spite of other people working on the project disagreeing. The "success" was announced by Perón on 24 March 1951, becoming the topic of newspaper stories around the world. While preparing for a ski trip to Aspen, Lyman Spitzer received a telephone call from his father, who mentioned an article on Huemul in The New York Times . Looking over
13575-636: The European Axis declaring war on the US. Japan conquered much of coastal China and Southeast Asia , but its advances in the Pacific were halted in mid-1942 after its defeat in the naval Battle of Midway ; Germany and Italy were defeated in North Africa and at Stalingrad in the Soviet Union. Key setbacks in 1943—including German defeats on the Eastern Front, the Allied invasions of Sicily and
13756-702: The French possessions of Syria and Lebanon , assisted by the Free French . With the situation in Europe and Asia relatively stable, Germany, Japan, and the Soviet Union made preparations for war. With the Soviets wary of mounting tensions with Germany, and the Japanese planning to take advantage of the European War by seizing resource-rich European possessions in Southeast Asia , the two powers signed
13937-486: The Germans, and the last large operational unit of the Polish Army surrendered on 6 October . Despite the military defeat, Poland never surrendered; instead, it formed the Polish government-in-exile and a clandestine state apparatus remained in occupied Poland. A significant part of Polish military personnel evacuated to Romania and Latvia; many of them later fought against the Axis in other theatres of
14118-512: The Nationalists. Both Germany and the Soviet Union used this proxy war as an opportunity to test in combat their most advanced weapons and tactics. The Nationalists won the civil war in April 1939; Franco, now dictator, remained officially neutral during World War II but generally favoured the Axis . His greatest collaboration with Germany was the sending of volunteers to fight on the Eastern Front . In July 1937, Japan captured
14299-511: The Royal Navy putting three Italian battleships out of commission after a carrier attack at Taranto , and neutralising several more warships at the Battle of Cape Matapan . Italian defeats prompted Germany to deploy an expeditionary force to North Africa; at the end of March 1941, Rommel 's Afrika Korps launched an offensive which drove back Commonwealth forces. In less than a month, Axis forces advanced to western Egypt and besieged
14480-602: The Soviet Union occupied the entire territories of Estonia, Latvia and Lithuania, as well as the Romanian regions of Bessarabia, Northern Bukovina, and the Hertsa region . In August 1940, Hitler imposed the Second Vienna Award on Romania which led to the transfer of Northern Transylvania to Hungary. In September 1940, Bulgaria demanded Southern Dobruja from Romania with German and Italian support, leading to
14661-767: The Soviet Union , opening the Eastern Front and initially making large territorial gains. Japan aimed to dominate East Asia and the Asia-Pacific , and by 1937 was at war with the Republic of China . In December 1941, Japan attacked American and British territories in Southeast Asia and the Central Pacific , including Pearl Harbor in Hawaii , which resulted in the US and the UK declaring war against Japan, and
14842-530: The Soviet Union and Mongolia . The Japanese doctrine of Hokushin-ron , which emphasised Japan's expansion northward, was favoured by the Imperial Army during this time. This policy would prove difficult to maintain in light of the Japanese defeat at Khalkin Gol in 1939, the ongoing Second Sino-Japanese War and ally Nazi Germany pursuing neutrality with the Soviets. Japan and the Soviet Union eventually signed
15023-756: The Soviet Union should be eliminated and aimed for the conquest of Ukraine , the Baltic states and Byelorussia . However, other senior German officials like Ribbentrop saw an opportunity to create a Euro-Asian bloc against the British Empire by inviting the Soviet Union into the Tripartite Pact. In November 1940, negotiations took place to determine if the Soviet Union would join the pact. The Soviets showed some interest but asked for concessions from Finland, Bulgaria, Turkey, and Japan that Germany considered unacceptable. On 18 December 1940, Hitler issued
15204-481: The UK reports, Princeton found itself in the position of trying to defend the stellarator as a useful experimental machine while other groups from around the US were clamoring for funds to build tokamaks. In July 1969 Gottlieb had a change of heart, offering to convert the Model C to a tokamak layout. In December it was shut down and reopened in May as the Symmetric Tokamak (ST). The ST immediately matched
15385-402: The US dropped the first atomic bombs on Hiroshima and Nagasaki on 6 and 9 August. Faced with an imminent invasion of the Japanese archipelago , the possibility of further atomic bombings, and the Soviet declaration of war against Japan and its invasion of Manchuria , Japan announced its unconditional surrender on 15 August and signed a surrender document on 2 September 1945 , marking
15566-581: The United Kingdom and France guaranteed their support for Polish independence ; when Italy conquered Albania in April 1939, the same guarantee was extended to the Kingdoms of Romania and Greece . Shortly after the Franco - British pledge to Poland, Germany and Italy formalised their own alliance with the Pact of Steel . Hitler accused the United Kingdom and Poland of trying to "encircle" Germany and renounced
15747-542: The United Kingdom attacked on 3 July in an attempt to prevent its seizure by Germany. The air Battle of Britain began in early July with Luftwaffe attacks on shipping and harbours . The German campaign for air superiority started in August but its failure to defeat RAF Fighter Command forced the indefinite postponement of the proposed German invasion of Britain . The German strategic bombing offensive intensified with night attacks on London and other cities in
15928-461: The United Kingdom. The Germans turned south against the weakened French army, and Paris fell to them on 14 June. Eight days later France signed an armistice with Germany ; it was divided into German and Italian occupation zones , and an unoccupied rump state under the Vichy Regime , which, though officially neutral, was generally aligned with Germany. France kept its fleet, which
16109-660: The United States was assisting China and the Western Allies, and had amended the Neutrality Act to allow "cash and carry" purchases by the Allies. In 1940, following the German capture of Paris, the size of the United States Navy was significantly increased . In September the United States further agreed to a trade of American destroyers for British bases . Still, a large majority of the American public continued to oppose any direct military intervention in
16290-606: The Yellow River ; this manoeuvre bought time for the Chinese to prepare their defences at Wuhan , but the city was taken by October. Japanese military victories did not bring about the collapse of Chinese resistance that Japan had hoped to achieve; instead, the Chinese government relocated inland to Chongqing and continued the war. In the mid-to-late 1930s, Japanese forces in Manchukuo had sporadic border clashes with
16471-408: The application of electric and/or magnetic fields through a gas. Plasma generated in a laboratory setting and for industrial use can be generally categorized by: Just like the many uses of plasma, there are several means for its generation. However, one principle is common to all of them: there must be energy input to produce and sustain it. For this case, plasma is generated when an electric current
16652-570: The ascent of a mountain." Two sections were initially set up, S Section working on the stellarator under Spitzer, and B Section working on bomb design under Wheeler. Matterhorn was set up at Princeton's new Forrestal Campus, a 825 acres (334 ha) plot of land the University purchased from the Rockefeller Institute for Medical Research when Rockefeller relocated to Manhattan . The land was located about 3 miles (4.8 km) from
16833-461: The capital Nanking in December 1937. After the fall of Nanking, tens or hundreds of thousands of Chinese civilians and disarmed combatants were murdered by the Japanese . In March 1938, Nationalist Chinese forces won their first major victory at Taierzhuang , but then the city of Xuzhou was taken by the Japanese in May. In June 1938, Chinese forces stalled the Japanese advance by flooding
17014-418: The center into one of the half-tori, exit into the center of the next tube, and so on. This particle will complete a loop around the entire reactor without leaving the center. Now consider another particle traveling parallel to the first, but initially located near the inside wall of the tube. In this case, it will enter the outside edge of the half-torus and begin to drift down. It exits that section and enters
17195-646: The characteristics of plasma were claimed to be difficult to obtain due to the high pressure, the passive effect of plasma on synthesis of different nanostructures clearly suggested the effective confinement. They also showed that upon maintaining the impermeability for a few tens of seconds, screening of ions at the plasma-gas interface could give rise to a strong secondary mode of heating (known as viscous heating) leading to different kinetics of reactions and formation of complex nanomaterials . World War II Asia-Pacific Mediterranean and Middle East Other campaigns Coups World War II or
17376-403: The conflict well into 1941. In December 1940, Roosevelt accused Hitler of planning world conquest and ruled out any negotiations as useless, calling for the United States to become an " arsenal of democracy " and promoting Lend-Lease programmes of military and humanitarian aid to support the British war effort; Lend-Lease was later extended to the other Allies, including the Soviet Union after it
17557-526: The creation of a " New Roman Empire ". Adolf Hitler , after an unsuccessful attempt to overthrow the German government in 1923, eventually became the Chancellor of Germany in 1933 when Paul von Hindenburg and the Reichstag appointed him. Following Hindenburg's death in 1934, Hitler proclaimed himself Führer of Germany and abolished democracy, espousing a radical, racially motivated revision of
17738-410: The critical threshold of breakeven would be reached in the early 1980s. What was needed was larger machines and more powerful systems to heat the plasma to fusion temperatures. Tokamaks are a type of pinch machine, differing from earlier designs primarily in the amount of current in the plasma: above a certain threshold known as the safety factor , or q , the plasma is much more stable. ZETA ran at
17919-450: The density). In thermal equilibrium , the relationship is given by the Saha equation . At low temperatures, ions and electrons tend to recombine into bound states—atoms —and the plasma will eventually become a gas. In most cases, the electrons and heavy plasma particles (ions and neutral atoms) separately have a relatively well-defined temperature; that is, their energy distribution function
18100-416: The description in the article, Spitzer concluded it could not possibly work; the system simply could not provide enough energy to heat the fuel to fusion temperatures. But the idea stuck with him, and he began considering systems that would work. While riding the ski lift , he hit upon the stellarator concept. The basic concept was a way to modify the torus layout so that it addressed Fermi's concerns through
18281-406: The design did not lie flat, the tori at either end had to be tilted. This meant the drift cancellation was further reduced, but again, calculations suggested the system would work. To understand how the system works to counteract drift, consider the path of a single particle in the system starting in one of the straight sections. If that particle is perfectly centered in the tube, it will travel down
18462-458: The design of the Model C device was becoming more defined. It emerged as a large racetrack-layout machine with multiple heating sources and a divertor, essentially an even larger B-66. Construction began in 1958 and was completed in 1961. It could be adjusted to allow a plasma minor axis between 5 and 7.5 centimetres (2.0 and 3.0 in) and was 1,200 cm (470 in) in length. The toroidal field coils normally operated at 35,000 gauss. By
18643-410: The device would essentially be cut in half to produce two half-tori. They would then be joined with two straight sections between the open ends. The key was that they were connected to alternate ends so that the right half of one of the tori was connected to the left of the other. The resulting design resembled a figure-8 when viewed from above. Because the straight tubes could not pass through each other,
18824-438: The device's geometry. By twisting one end of the torus compared to the other, forming a figure-8 layout instead of a circle, the magnetic lines no longer travelled around the tube at a constant radius, instead they moved closer and further from the torus' center. A particle orbiting these lines would find itself constantly moving in and out across the minor axis of the torus. The drift upward while it travelled through one section of
19005-452: The discharge forms a luminous arc, where the inter-electrode material (usually, a gas) undergoes various stages — saturation, breakdown, glow, transition, and thermal arc. The voltage rises to its maximum in the saturation stage, and thereafter it undergoes fluctuations of the various stages, while the current progressively increases throughout. Electrical resistance along the arc creates heat , which dissociates more gas molecules and ionizes
19186-757: The dissolution of the Austro-Hungarian, Ottoman, and Russian Empires. To prevent a future world war, the League of Nations was established in 1920 by the Paris Peace Conference . The organisation's primary goals were to prevent armed conflict through collective security, military, and naval disarmament , as well as settling international disputes through peaceful negotiations and arbitration. Despite strong pacifist sentiment after World War I , irredentist and revanchist nationalism had emerged in several European states. These sentiments were especially marked in Germany because of
19367-577: The distant stars , and much of interstellar space or intergalactic space is also filled with plasma, albeit at very low densities. Astrophysical plasmas are also observed in accretion disks around stars or compact objects like white dwarfs , neutron stars , or black holes in close binary star systems. Plasma is associated with ejection of material in astrophysical jets , which have been observed with accreting black holes or in active galaxies like M87's jet that possibly extends out to 5,000 light-years. Most artificial plasmas are generated by
19548-438: The electric force and the good conductivity of plasmas usually ensure that the densities of positive and negative charges in any sizeable region are equal ("quasineutrality"). A plasma with a significant excess of charge density, or, in the extreme case, is composed of a single species, is called a non-neutral plasma . In such a plasma, electric fields play a dominant role. Examples are charged particle beams , an electron cloud in
19729-537: The electron density n e {\displaystyle n_{e}} , that is, the number of charge-contributing electrons per unit volume. The degree of ionization α {\displaystyle \alpha } is defined as fraction of neutral particles that are ionized: α = n i n i + n n , {\displaystyle \alpha ={\frac {n_{i}}{n_{i}+n_{n}}},} where n i {\displaystyle n_{i}}
19910-662: The end of May completed the German conquest of the Balkans. Partisan warfare subsequently broke out against the Axis occupation of Yugoslavia , which continued until the end of the war. In the Middle East in May, Commonwealth forces quashed an uprising in Iraq which had been supported by German aircraft from bases within Vichy-controlled Syria . Between June and July, British-led forces invaded and occupied
20091-463: The end of the war. World War II changed the political alignment and social structure of the world, and it set the foundation of international relations for the rest of the 20th century and into the 21st century. The United Nations was established to foster international cooperation and prevent conflicts, with the victorious great powers—China, France, the Soviet Union, the UK, and the US—becoming
20272-479: The energy released by the fusion reaction is much greater than what it takes to start it, even a small number of reactions can heat surrounding fuel until it fuses as well. In 1944, Enrico Fermi calculated the D-T reaction would be self-sustaining at about 50,000,000 degrees Celsius (90,000,000 degrees Fahrenheit). Materials heated beyond a few tens of thousand degrees ionize into their electrons and nuclei , producing
20453-454: The figure on the right). The first impact of an electron on an atom results in one ion and two electrons. Therefore, the number of charged particles increases rapidly (in the millions) only "after about 20 successive sets of collisions", mainly due to a small mean free path (average distance travelled between collisions). Electric arc is a continuous electric discharge between two electrodes, similar to lightning . With ample current density,
20634-490: The filamentation generated plasma is the relatively low ion density due to defocusing effects of the ionized electrons. (See also Filament propagation ) Impermeable plasma is a type of thermal plasma which acts like an impermeable solid with respect to gas or cold plasma and can be physically pushed. Interaction of cold gas and thermal plasma was briefly studied by a group led by Hannes Alfvén in 1960s and 1970s for its possible applications in insulation of fusion plasma from
20815-575: The first step of what its government saw as the country's right to rule Asia , staged the Mukden incident as a pretext to invade Manchuria and establish the puppet state of Manchukuo . China appealed to the League of Nations to stop the Japanese invasion of Manchuria. Japan withdrew from the League of Nations after being condemned for its incursion into Manchuria. The two nations then fought several battles, in Shanghai , Rehe and Hebei , until
20996-475: The first to achieve fusion on Earth, using a particle accelerator to shoot deuterium nuclei into a metal foil containing deuterium , lithium or other elements. These experiments allowed them to measure the nuclear cross section of various reactions of fusion between nuclei, and determined that the tritium-deuterium reaction occurred at a lower energy than any other fuel, peaking at about 100,000 electronvolts (100 keV). 100 keV corresponds to
21177-864: The former Chinese imperial capital of Peking after instigating the Marco Polo Bridge incident , which culminated in the Japanese campaign to invade all of China. The Soviets quickly signed a non-aggression pact with China to lend materiel support, effectively ending China's prior cooperation with Germany . From September to November, the Japanese attacked Taiyuan , engaged the Kuomintang Army around Xinkou , and fought Communist forces in Pingxingguan . Generalissimo Chiang Kai-shek deployed his best army to defend Shanghai , but after three months of fighting, Shanghai fell. The Japanese continued to push Chinese forces back, capturing
21358-551: The heating systems were used that slowly increased the temperatures. Notable among these was the 1964 addition of a small particle accelerator to accelerate fuel ions to high enough energy to cross the magnetic fields, depositing energy within the reactor when they collided with other ions already inside. This method of heating, now known as neutral beam injection , has since become almost universal on magnetic confinement fusion machines. Model C spent most of its history involved in studies of ion transport. Through continual tuning of
21539-416: The interaction with the magnetic field can form a magnetic rope structure. (See also Plasma pinch ) Filamentation also refers to the self-focusing of a high power laser pulse. At high powers, the nonlinear part of the index of refraction becomes important and causes a higher index of refraction in the center of the laser beam, where the laser is brighter than at the edges, causing a feedback that focuses
21720-525: The invasion of the Ethiopian Empire (also known as Abyssinia ) by the armed forces of the Kingdom of Italy ( Regno d'Italia ), which was launched from Italian Somaliland and Eritrea . The war resulted in the military occupation of Ethiopia and its annexation into the newly created colony of Italian East Africa ( Africa Orientale Italiana , or AOI); in addition it exposed the weakness of
21901-411: The ions and electrons. Spitzer introduced the concept of a divertor , a magnet placed around the tube that pulled off the very outer layer of the plasma. This would remove the ions before they drifted too far and hit the walls. It would also remove any heavier elements in the plasma. Plasma (physics) Plasma (from Ancient Greek πλάσμα ( plásma ) 'moldable substance' )
22082-410: The laser even more. The tighter focused laser has a higher peak brightness (irradiance) that forms a plasma. The plasma has an index of refraction lower than one, and causes a defocusing of the laser beam. The interplay of the focusing index of refraction, and the defocusing plasma makes the formation of a long filament of plasma that can be micrometers to kilometers in length. One interesting aspect of
22263-682: The latter enabling the strategic bombing of population centres and delivery of the only two nuclear weapons ever used in war. World War II was the deadliest conflict in history, resulting in 70 to 85 million deaths , more than half being civilians. Millions died in genocides , including the Holocaust of European Jews, as well as from massacres, starvation, and disease. Following the Allied powers' victory, Germany , Austria , Japan , and Korea were occupied, and war crimes tribunals were conducted against German and Japanese leaders . The causes of World War II included unresolved tensions in
22444-436: The long axis of the tube. But, as Fermi pointed out, when the solenoid is bent into a ring, the electrical windings would be closer together on the inside than the outside. This would lead to an uneven field across the tube, and the fuel will slowly drift out of the center. Since the electrons and ions would drift in opposite directions, this would lead to a charge separation and electrostatic forces that would eventually overwhelm
22625-523: The machines for themselves. Their tests, made using a laser -based system developed for the ZETA reactor in England, verified the Soviet claims of electron temperatures of 1,000 eV. What followed was a "veritable stampede" of tokamak construction worldwide. At first the US labs ignored the tokamak; Spitzer himself dismissed it out of hand as experimental error. However, as new results came in, especially
22806-441: The magnetic force. Some additional force needs to counteract this drift, providing long-term confinement . Spitzer's key concept in the stellarator design is that the drift that Fermi noted could be canceled out through the physical arrangement of the vacuum tube. In a torus, particles on the inside edge of the tube, where the field was stronger, would drift up, while those on the outside would drift down (or vice versa). However, if
22987-431: The magnetic lines, they would do so in opposite directions, and at very high rotational speeds. This leads to the possibility of collisions between particles circling different lines of force as they circulate through the reactor, which due to purely geometric reasons, causes the fuel to slowly drift outward. This process eventually causes the fuel to either collide with the structure or cause a large charge separation between
23168-467: The magnetic system and the addition of the new heating methods, in 1969, Model C eventually reached electron temperatures of 400 eV. Through this period, a number of new potential stellarator designs emerged, which featured a simplified magnetic layout. The Model C used separate confinement and helical coils, as this was an evolutionary process from the original design which had only the confinement coils. Other researchers, notably in Germany, noted that
23349-497: The main Princeton campus and already had sixteen laboratory buildings. Spitzer set up the top-secret S Section in a former rabbit hutch. It was not long before the other labs began agitating for their own funding. Tuck had managed to arrange some funding for his Perhapsatron through some discretionary budgets at LANL, but other teams at LANL, Berkeley and Oak Ridge (ORNL) also presented their ideas. The AEC eventually organized
23530-625: The mid-1960s, Spitzer was convinced that the stellarator was matching the Bohm diffusion rate, which suggested it would never be a practical fusion device. The release of information on the USSR's tokamak design in 1968 indicated a leap in performance. After debate within the US industry, PPPL converted the Model C stellarator to the Symmetrical Tokamak (ST) as a way to confirm or deny these results. ST confirmed them, and large-scale work on
23711-463: The net field, a second set of coils running poloidally around the outside of the helical magnet produces a second vertical field that mixes with the helical one. The result is a much simpler layout, as the poloidal magnets are generally much smaller and there is ample room between them to reach the interior, whereas in the original layout the toroidal confinement magnets are relatively large and leave little room between them. A further update emerged from
23892-417: The next few months, Spitzer produced a series of reports outlining the conceptual basis for the stellarator, as well as potential problems. The series is notable for its depth; it not only included a detailed analysis of the mathematics of the plasma and stability but also outlined a number of additional problems like heating the plasma and dealing with impurities. With this work in hand, Spitzer began to lobby
24073-399: The overall field layout by replacing the elements. These "modular coils" are now a major part of ongoing research. In 1968, scientists in the Soviet Union released the results of their tokamak machines, notably their newest example, T-3. The results were so startling that there was widespread scepticism. To address this, the Soviets invited a team of experts from the United Kingdom to test
24254-400: The particle were made to alternate between the inside and outside of the tube, the drifts would alternate between up and down and would cancel out. The cancellation is not perfect, leaving some net drift, but basic calculations suggested drift would be lowered enough to confine plasma long enough to heat it sufficiently. Spitzer's suggestion for doing this was simple. Instead of a normal torus,
24435-444: The particles to travel without rotation. B-65, completed in 1957, was built using the new "racetrack" layout. This was the result of the observation that adding helical coils to the curved portions of the device produced a field that introduced the rotation purely through the resulting magnetic fields. This had the added advantage that the magnetic field included shear , which was known to improve stability. B-3, also completed in 1957,
24616-406: The performance being seen in the Soviet machines, besting the Model C's results by over ten times. From that point, PPPL was the primary developer of the tokamak approach in the US, introducing a series of machines to test various designs and modifications. The Princeton Large Torus of 1975 quickly hit several performance numbers that were required for a commercial machine, and it was widely believed
24797-502: The permanent members of its security council . The Soviet Union and the United States emerged as rival superpowers , setting the stage for the Cold War . In the wake of European devastation, the influence of its great powers waned, triggering the decolonisation of Africa and Asia . Most countries whose industries had been damaged moved towards economic recovery and expansion . World War II began in Europe on 1 September 1939 with
24978-474: The plasma as a single fluid governed by a combination of Maxwell's equations and the Navier–Stokes equations . A more general description is the two-fluid plasma, where the ions and electrons are described separately. Fluid models are often accurate when collisionality is sufficiently high to keep the plasma velocity distribution close to a Maxwell–Boltzmann distribution . Because fluid models usually describe
25159-403: The plasma circle the magnetic lines of force. One way to provide some confinement would be to place a tube of fuel inside the open core of a solenoid . A solenoid creates magnetic lines running down its center, and fuel would be held away from the walls by orbiting these lines of force. But such an arrangement does not confine the plasma along the length of the tube. The obvious solution is to bend
25340-426: The plasma high conductivity, the electric field associated with a plasma moving with velocity v {\displaystyle \mathbf {v} } in the magnetic field B {\displaystyle \mathbf {B} } is given by the usual Lorentz formula E = − v × B {\displaystyle \mathbf {E} =-\mathbf {v} \times \mathbf {B} } , and
25521-501: The plasma in terms of a single flow at a certain temperature at each spatial location, they can neither capture velocity space structures like beams or double layers , nor resolve wave-particle effects. Kinetic models describe the particle velocity distribution function at each point in the plasma and therefore do not need to assume a Maxwell–Boltzmann distribution . A kinetic description is often necessary for collisionless plasmas. There are two common approaches to kinetic description of
25702-488: The plasma potential due to what is termed a Debye sheath . The good electrical conductivity of plasmas makes their electric fields very small. This results in the important concept of "quasineutrality", which says the density of negative charges is approximately equal to the density of positive charges over large volumes of the plasma ( n e = ⟨ Z ⟩ n i {\displaystyle n_{e}=\langle Z\rangle n_{i}} ), but on
25883-495: The plasma ring inside the torus to expand until it hit the walls of the reactor. After World War II , a number of researchers began considering different ways to confine a plasma. George Paget Thomson of Imperial College London proposed a system now known as z-pinch , which runs a current through the plasma. Due to the Lorentz force , this current creates a magnetic field that pulls the plasma in on itself, keeping it away from
26064-415: The point that long-range electric and magnetic fields dominate its behaviour. Plasma is typically an electrically quasineutral medium of unbound positive and negative particles (i.e., the overall charge of a plasma is roughly zero). Although these particles are unbound, they are not "free" in the sense of not experiencing forces. Moving charged particles generate electric currents , and any movement of
26245-589: The political European map with the defeat of the Central Powers —including Austria-Hungary , Germany , Bulgaria , and the Ottoman Empire —and the 1917 Bolshevik seizure of power in Russia , which led to the founding of the Soviet Union. Meanwhile, the victorious Allies of World War I , such as France, Belgium, Italy, Romania, and Greece, gained territory, and new nation-states were created out of
26426-599: The port of Tobruk . By late March 1941, Bulgaria and Yugoslavia signed the Tripartite Pact ; however, the Yugoslav government was overthrown two days later by pro-British nationalists. Germany and Italy responded with simultaneous invasions of both Yugoslavia and Greece , commencing on 6 April 1941; both nations were forced to surrender within the month. The airborne invasion of the Greek island of Crete at
26607-616: The power of the magnetic fields, requiring superconducting magnets and huge confinement volumes. The cost of such a machine was such that the involved parties banded together to begin the ITER project. As the problems with the tokamak approach grew, interest in the stellarator approach reemerged. This coincided with the development of advanced computer aided planning tools that allowed the construction of complex magnets that were previously known but considered too difficult to design and build. New materials and construction methods have increased
26788-620: The quality and power of the magnetic fields, improving performance. New devices have been built to test these concepts. Major examples include Wendelstein 7-X in Germany, the Helically Symmetric Experiment (HSX) in the US, and the Large Helical Device in Japan. W7X and LHD use superconducting magnetic coils . The lack of an internal current eliminates some of the instabilities of the tokamak, meaning
26969-454: The reactor walls. However, later it was found that the external magnetic fields in this configuration could induce kink instabilities in the plasma and subsequently lead to an unexpectedly high heat loss to the walls. In 2013, a group of materials scientists reported that they have successfully generated stable impermeable plasma with no magnetic confinement using only an ultrahigh-pressure blanket of cold gas. While spectroscopic data on
27150-435: The reactor would be reversed after half an orbit and it would drift downward again. The cancellation was not perfect, but it appeared this would so greatly reduce the net drift rates that the fuel would remain trapped long enough to heat it to the required temperatures. His 1958 description was simple and direct: Magnetic confinement in the stellarator is based on a strong magnetic field produced by solenoidal coils encircling
27331-433: The realization that the total field could be produced through a series of independent magnets shaped like the local field. This results in a series of complex magnets that are arranged like the toroidal coils of the original layout. The advantage of this design is that the magnets are entirely independent; if one is damaged it can be individually replaced without affecting the rest of the system. Additionally, one can re-arrange
27512-722: The remainder of Czechoslovakia and subsequently split it into the German Protectorate of Bohemia and Moravia and a pro-German client state , the Slovak Republic . Hitler also delivered an ultimatum to Lithuania on 20 March 1939, forcing the concession of the Klaipėda Region , formerly the German Memelland . Greatly alarmed and with Hitler making further demands on the Free City of Danzig ,
27693-665: The resulting atoms. Therefore, the electrical energy is given to electrons, which, due to their great mobility and large numbers, are able to disperse it rapidly by elastic collisions to the heavy particles. Plasmas find applications in many fields of research, technology and industry, for example, in industrial and extractive metallurgy , surface treatments such as plasma spraying (coating), etching in microelectronics, metal cutting and welding ; as well as in everyday vehicle exhaust cleanup and fluorescent / luminescent lamps, fuel ignition, and even in supersonic combustion engines for aerospace engineering . A world effort
27874-423: The same overall magnetic field configuration could be achieved with a much simpler arrangement. This led to the torsatron or heliotron layout. In these designs, the primary field is produced by a single helical magnet, similar to one of the helical windings of the "classical" stellarator. In contrast to those systems, only a single magnet is needed, and it is much larger than those in the stellarators. To produce
28055-757: The scale of the Debye length , there can be charge imbalance. In the special case that double layers are formed, the charge separation can extend some tens of Debye lengths. The magnitude of the potentials and electric fields must be determined by means other than simply finding the net charge density . A common example is to assume that the electrons satisfy the Boltzmann relation : n e ∝ exp ( e Φ / k B T e ) . {\displaystyle n_{e}\propto \exp(e\Phi /k_{\text{B}}T_{e}).} Differentiating this relation provides
28236-420: The second straight section, still on the outside edge of that tube. However, because the tubes are crossed, when it reaches the second half-torus it enters it on the inside edge. As it travels through this section it drifts back up. This effect would reduce one of the primary causes of drift in the machine, but there were others to consider as well. Although the ions and electrons in the plasma would both circle
28417-404: The sense that only a tiny fraction of the gas molecules are ionized. These kinds of weakly ionized gases are also nonthermal "cold" plasmas. In the presence of magnetics fields, the study of such magnetized nonthermal weakly ionized gases involves resistive magnetohydrodynamics with low magnetic Reynolds number , a challenging field of plasma physics where calculations require dyadic tensors in
28598-425: The sides. Unfortunately, this arrangement would not confine the plasma along the length of the tube, and the plasma would be free to flow out the ends. The obvious solution to this problem is to bend the tube around into a torus (a ring or donut) shape. Motion towards the sides remains constrained as before, and while the particles remain free to move along the lines, in this case, they will simply circulate around
28779-410: The significant territorial, colonial, and financial losses imposed by the Treaty of Versailles . Under the treaty, Germany lost around 13 percent of its home territory and all its overseas possessions , while German annexation of other states was prohibited, reparations were imposed, and limits were placed on the size and capability of the country's armed forces . The German Empire was dissolved in
28960-408: The simple torus. This led to the construction of the Model B, which had the problem that the magnets were not well mounted and tended to move around when they were powered to their maximum capacity of 50,000 gauss. A second design also failed for the same reason, but this machine demonstrated several-hundred-kilovolt X-rays that suggested good confinement. The lessons from these two designs led to
29141-498: The start or prelude to World War II. The exact date of the war's end also is not universally agreed upon. It was generally accepted at the time that the war ended with the armistice of 15 August 1945 ( V-J Day ), rather than with the formal surrender of Japan on 2 September 1945, which officially ended the war in Asia . A peace treaty between Japan and the Allies was signed in 1951. A 1990 treaty regarding Germany's future allowed
29322-561: The stellarator concept ended in the US replaced by tokamaks. Research continued in Germany and Japan, where several new designs were built. The tokamak ultimately proved to have problems similar to the stellarators, but for different reasons. Since the 1990s, the stellarator design has seen renewed interest. New methods of construction have increased the quality and power of the magnetic fields, improving performance. A number of new devices have been built to test these concepts. In 1934, Mark Oliphant , Paul Harteck and Ernest Rutherford were
29503-601: The stellarator should be more stable at similar operating conditions. On the downside, since it lacks the confinement provided by the current found in a tokamak, the stellarator requires more powerful magnets to reach any given confinement. The stellarator is an inherently steady-state machine, which has several advantages from an engineering standpoint. As part of a renewed push for fusion power from around 2018, private sector stellarator projects have emerged and in number compete with, though are much less developed than, tokamak projects, such as Renaissance Fusion and Proxima Fusion,
29684-593: The strong Maginot Line fortifications on the Franco-German border, Germany directed its attack at the neutral nations of Belgium , the Netherlands , and Luxembourg . The Germans carried out a flanking manoeuvre through the Ardennes region, which was mistakenly perceived by the Allies as an impenetrable natural barrier against armoured vehicles. By successfully implementing new Blitzkrieg tactics,
29865-411: The time Model C began operations, information collected from previous machines was making it clear that it would not be able to produce large-scale fusion. Ion transport across the magnetic field lines was much higher than classical theory suggested. Greatly increased magnetic fields of the later machines did little to address this, and confinement times simply were not improving. Attention began to turn to
30046-481: The tube around into a torus (donut) shape, so that any one line forms a circle, and the particles can circle forever. However, this solution does not actually work. For purely geometric reasons, the magnets ringing the torus are closer together on the inside curve, inside the "donut hole". Fermi noted this would cause the electrons to drift away from the nuclei, eventually causing them to separate and cause large voltages to develop. The resulting electric field would cause
30227-536: The two wars became World War II in 1941. Other proposed starting dates for World War II include the Italian invasion of Abyssinia on 3 October 1935. The British historian Antony Beevor views the beginning of World War II as the Battles of Khalkhin Gol fought between Japan and the forces of Mongolia and the Soviet Union from May to September 1939. Others view the Spanish Civil War as
30408-581: The walls of the reactor. This eliminates the need for magnets on the outside, avoiding the problem Fermi noted. Various teams in the UK had built a number of small experimental devices using this technique by the late 1940s. Another person working on controlled fusion reactors was Ronald Richter , a German scientist who moved to Argentina after the war. His thermotron used a system of electrical arcs and mechanical compression (sound waves) for heating and confinement. He convinced Juan Perón to fund development of an experimental reactor on an isolated island near
30589-513: The war were not fulfilled in the peace settlement. From 1922 to 1925, the Fascist movement led by Benito Mussolini seized power in Italy with a nationalist, totalitarian , and class collaborationist agenda that abolished representative democracy, repressed socialist, left-wing, and liberal forces, and pursued an aggressive expansionist foreign policy aimed at making Italy a world power, promising
30770-475: The war. Germany annexed western Poland and occupied central Poland ; the Soviet Union annexed eastern Poland ; small shares of Polish territory were transferred to Lithuania and Slovakia . On 6 October, Hitler made a public peace overture to the United Kingdom and France but said that the future of Poland was to be determined exclusively by Germany and the Soviet Union. The proposal was rejected and Hitler ordered an immediate offensive against France, which
30951-512: The west halted the German advance for several days, but it was outflanked and encircled by the Wehrmacht . Remnants of the Polish army broke through to besieged Warsaw . On 17 September 1939, two days after signing a cease-fire with Japan , the Soviet Union invaded Poland under the supposed pretext that the Polish state had ceased to exist. On 27 September, the Warsaw garrison surrendered to
31132-483: The world order , and soon began a massive rearmament campaign . France, seeking to secure its alliance with Italy, allowed Italy a free hand in Ethiopia , which Italy desired as a colonial possession. The situation was aggravated in early 1935 when the Territory of the Saar Basin was legally reunited with Germany, and Hitler repudiated the Treaty of Versailles, accelerated his rearmament programme, and introduced conscription. The United Kingdom, France and Italy formed
31313-554: Was invaded by Germany. The United States started strategic planning to prepare for a full-scale offensive against Germany. At the end of September 1940, the Tripartite Pact formally united Japan, Italy, and Germany as the Axis powers . The Tripartite Pact stipulated that any country—with the exception of the Soviet Union—that attacked any Axis Power would be forced to go to war against all three. The Axis expanded in November 1940 when Hungary , Slovakia , and Romania joined. Romania and Hungary later made major contributions to
31494-400: Was a greatly enlarged B-2 machine with ultra-high vacuum and pulsed confinement up to 50,000 gauss and projected confinement times as long as 0.01 second. The last of the B-series machines was the B-66, completed in 1958, which was essentially a combination of the racetrack layout from B-65 with the larger size and energy of the B-3. Unfortunately, all of these larger machines demonstrated
31675-422: Was carried out by Spitzer's team at what became the Princeton Plasma Physics Laboratory (PPPL). Spitzer's Model A began operation in 1953 and demonstrated plasma confinement. Larger models followed, but demonstrated poor performance, losing plasma at rates far worse than theoretical predictions. By the early 1960s, hopes of producing a commercial machine faded, and attention turned to studying fundamental theory. By
31856-403: Was postponed until the spring of 1940 due to bad weather. After the outbreak of war in Poland, Stalin threatened Estonia , Latvia , and Lithuania with military invasion, forcing the three Baltic countries to sign pacts allowing the creation of Soviet military bases in these countries; in October 1939, significant Soviet military contingents were moved there. Finland refused to sign
32037-458: Was promoting the stellarator, he also travelled to Washington to propose building a pinch device. He considered Spitzer's plans "incredibly ambitious." Nevertheless, Spitzer was successful in gaining $ 50,000 in funding from the AEC, while Tuck received nothing. The Princeton program was officially created on 1 July 1951. Spitzer, an avid mountain climber, proposed the name " Project Matterhorn " because he felt "the work at hand seemed difficult, like
32218-657: Was repulsed with heavy Italian casualties; the campaign ended within months with minor territorial changes. To assist Italy and prevent Britain from gaining a foothold, Germany prepared to invade the Balkans, which would threaten Romanian oil fields and strike against British dominance of the Mediterranean. In December 1940, British Empire forces began counter-offensives against Italian forces in Egypt and Italian East Africa . The offensives were successful; by early February 1941, Italy had lost control of eastern Libya, and large numbers of Italian troops had been taken prisoner. The Italian Navy also suffered significant defeats, with
32399-441: Was required to go through the bureaucracy of the League of Nations, which rendered it essentially toothless. The United States, concerned with events in Europe and Asia, passed the Neutrality Act in August of the same year. Hitler defied the Versailles and Locarno Treaties by remilitarising the Rhineland in March 1936, encountering little opposition due to the policy of appeasement . In October 1936, Germany and Italy formed
32580-469: Was sent to the Atoms for Peace show in Geneva . However, when the heating system was modified, the coupling increased dramatically, demonstrating temperatures within the heating section as high as 1,000 electronvolts (160 aJ). Two additional machines were built to study pulsed operation. B-64 was completed in 1955, essentially a larger version of the B-1 machine but powered by pulses of current that produced up to 15,000 gauss. This machine included
32761-731: Was triggered in the 1960s to study magnetohydrodynamic converters in order to bring MHD power conversion to market with commercial power plants of a new kind, converting the kinetic energy of a high velocity plasma into electricity with no moving parts at a high efficiency . Research was also conducted in the field of supersonic and hypersonic aerodynamics to study plasma interaction with magnetic fields to eventually achieve passive and even active flow control around vehicles or projectiles, in order to soften and mitigate shock waves , lower thermal transfer and reduce drag . Such ionized gases used in "plasma technology" ("technological" or "engineered" plasmas) are usually weakly ionized gases in
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