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58-813: In spectroscopy, the Hohlraum effect occurs when an object achieves thermodynamic equilibrium with an enclosing hohlraum. As a consequence of Kirchhoff’s law , everything optically blends together and contrast between the walls and the object effectively disappears. Hohlraums are used in High Energy Density Physics (HEDP) and Inertial Confinement Fusion (ICF) experiments to convert laser energy to thermal x-rays for imploding capsules, heating targets, and generating thermal radiation waves. They may also be used in Nuclear Weapon designs. The indirect drive approach to inertial confinement fusion

116-608: A spectral radiance that Kirchhoff labeled I (for specific intensity , the traditional name for spectral radiance). The precise mathematical expression for that universal function I was very much unknown to Kirchhoff, and it was just postulated to exist, until its precise mathematical expression was found in 1900 by Max Planck . It is nowadays referred to as Planck's law. Then, at each wavelength, for thermodynamic equilibrium in an enclosure, opaque to heat rays, with walls that absorb some radiation at every wavelength: Time reversibility A mathematical or physical process

174-461: A body nearly black. Some other materials are nearly black in particular wavelength bands. Such materials do not survive all the very high temperatures that are of interest. An improvement on lamp-black is found in manufactured carbon nanotubes. Nano-porous materials can achieve refractive indices nearly that of vacuum, in one case obtaining average reflectance of 0.045%. Bodies that are opaque to thermal radiation that falls on them are valuable in

232-404: A cavity can be made of opaque materials that absorb significant amounts of radiation at all wavelengths. It is not necessary that every part of the interior walls be a good absorber at every wavelength. The effective range of absorbing wavelengths can be extended by the use of patches of several differently absorbing materials in parts of the interior walls of the cavity. In thermodynamic equilibrium

290-469: A certain form of thermal equilibrium with the Hohlraum, when the spectral input into the resonator equals the spectral output at the resonance frequency. Next, suppose there are two Hohlraums at the same fixed temperature T {\displaystyle T} , then Planck argued that the thermal equilibrium of the small resonator is the same when connected to either Hohlraum. For, we can disconnect

348-523: A good approximation to a black surface, but will not be perfectly Lambertian, and must be viewed from nearly right angles to get the best properties. The construction of such devices was an important step in the empirical measurements that led to the precise mathematical identification of Kirchhoff's universal function, now known as Planck's law . Planck also noted that the perfect black bodies of Kirchhoff do not occur in physical reality. They are theoretical fictions. Kirchhoff's perfect black bodies absorb all

406-651: A good reflector must be a poor absorber. This is why, for example, lightweight emergency thermal blankets are based on reflective metallic coatings : they lose little heat by radiation. Kirchhoff's great insight was to recognize the universality and uniqueness of the function that describes the black body emissive power. But he did not know the precise form or character of that universal function. Attempts were made by Lord Rayleigh and Sir James Jeans 1900–1905 to describe it in classical terms, resulting in Rayleigh–Jeans law . This law turned out to be inconsistent yielding

464-427: A resonator tuned at ν 2 {\displaystyle \nu _{2}} , then detach and attach to another Hohlraum at the same temperature, thus transporting energy from one to another, violating the second law. We may apply the same argument for polarization and direction of radiation, obtaining the full principle of detailed balance. It has long been known that a lamp-black coating will make

522-470: A second system, a cavity with walls that are opaque, rigid, and not perfectly reflective to any wavelength, to be brought into connection, through an optical filter, with the blackbody enclosure, both at the same temperature. Radiation can pass from one system to the other. For example, suppose in the second system, the density of photons at narrow frequency band around wavelength λ {\displaystyle \lambda } were higher than that of

580-413: A similar, but more complicated argument, it can be shown that, since black-body radiation is equal in every direction (isotropic), the emissivity and the absorptivity, if they happen to be dependent on direction, must again be equal for any given direction. Average and overall absorptivity and emissivity data are often given for materials with values which differ from each other. For example, white paint

638-612: A temperature difference, violating the second law. Finally, suppose we have a material that violates Kirchhoff's law in detail , such that such that the total coefficient of absorption is not equal to the coefficient of emission at a certain T {\displaystyle T} and at a certain frequency ν {\displaystyle \nu } , then since it does not violate Kirchhoff's law when integrated, there must exist two frequencies ν 1 ≠ ν 2 {\displaystyle \nu _{1}\neq \nu _{2}} , such that

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696-405: A uniform implosion . The hohlraum walls must have surface roughness less than 1 micron, and hence accurate machining is required during fabrication. Any imperfection of the hohlraum wall during fabrication will cause uneven and non-symmetrical compression of the fuel capsule inside the hohlraum during inertial confinement fusion. Hence imperfection is to be carefully prevented so surface finishing

754-671: A way as to maintain the black body distribution. Hence absorptivity and emissivity must be equal. The absorptivity α λ {\displaystyle \alpha _{\lambda }} of the wall is the ratio of the energy absorbed by the wall to the energy incident on the wall, for a particular wavelength. Thus the absorbed energy is α λ E b λ ( λ , T ) {\displaystyle \alpha _{\lambda }E_{b\lambda }(\lambda ,T)} where E b λ ( λ , T ) {\displaystyle E_{b\lambda }(\lambda ,T)}

812-428: Is time-reversible if the dynamics of the process remain well-defined when the sequence of time-states is reversed. A deterministic process is time-reversible if the time-reversed process satisfies the same dynamic equations as the original process; in other words, the equations are invariant or symmetrical under a change in the sign of time. A stochastic process is reversible if the statistical properties of

870-455: Is a mathematical surface belonging jointly to the two media that touch it. It is the site of refraction of radiation that penetrates it and of reflection of radiation that does not. As such it obeys the Helmholtz reciprocity principle. The opaque body is considered to have a material interior that absorbs all and scatters or transmits none of the radiation that reaches it through refraction at

928-519: Is a special case of Onsager reciprocal relations as a consequence of the time reversibility of microscopic dynamics, also known as microscopic reversibility . A body at temperature T radiates electromagnetic energy . A perfect black body in thermodynamic equilibrium absorbs all light that strikes it, and radiates energy according to a unique law of radiative emissive power for temperature T ( Stefan–Boltzmann law ), universal for all perfect black bodies. Kirchhoff's law states that: Here,

986-540: Is also a poor emitter of green light. In other words, if a material, illuminated by black-body radiation of temperature T {\displaystyle T} , is dark at a certain frequency ν {\displaystyle \nu } , then its thermal radiation will also be dark at the same frequency ν {\displaystyle \nu } and the same temperature T {\displaystyle T} . More generally, all intensive properties are balanced in detail. So for example,

1044-473: Is as follows: the fusion fuel capsule is held inside a cylindrical hohlraum. The hohlraum body is manufactured using a high-Z (high atomic number) element, usually gold or uranium. Inside the hohlraum is a fuel capsule containing deuterium and tritium (D-T) fuel. A frozen layer of D-T ice adheres inside the fuel capsule. The fuel capsule wall is synthesized using light elements such as plastic, beryllium, or high density carbon, i.e. diamond. The outer portion of

1102-405: Is beyond the capability of any human being (or artificial intelligence ), and the macroscopic properties (like entropy and temperature) of many-body system are only defined from the statistics of the ensembles . When we talk about such macroscopic properties in thermodynamics, in certain cases, we can see irreversibility in the time evolution of these quantities on a statistical level. Indeed,

1160-417: Is extremely important, as during ICF laser shots, due to intense pressure and temperature, results are highly susceptible to hohlraum texture roughness. The fuel capsule must be precisely spherical, with texture roughness less than one nanometer, for fusion ignition to start. Otherwise, instability will cause fusion to fizzle. The fuel capsule contains a small fill hole with less than 5 microns diameter to inject

1218-975: Is quoted as having an absorptivity of 0.16, while having an emissivity of 0.93. This is because the absorptivity is averaged with weighting for the solar spectrum, while the emissivity is weighted for the emission of the paint itself at normal ambient temperatures. The absorptivity quoted in such cases is being calculated by: α s u n = ∫ 0 ∞ α λ ( λ ) I λ s u n ( λ ) d λ ∫ 0 ∞ I λ s u n ( λ ) d λ {\displaystyle \alpha _{\mathrm {sun} }=\displaystyle {\frac {\int _{0}^{\infty }\alpha _{\lambda }(\lambda )I_{\lambda \mathrm {sun} }(\lambda )\,d\lambda }{\int _{0}^{\infty }I_{\lambda \mathrm {sun} }(\lambda )\,d\lambda }}} while

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1276-453: Is the emission spectrum of the sun, and ε λ E b λ ( λ , T ) {\displaystyle \varepsilon _{\lambda }E_{b\lambda }(\lambda ,T)} is the emission spectrum of the paint. Although, by Kirchhoff's law, ε λ = α λ {\displaystyle \varepsilon _{\lambda }=\alpha _{\lambda }} in

1334-464: Is the emissivity at wavelength λ {\displaystyle \lambda } . For the maintenance of thermal equilibrium, these two quantities must be equal, or else the distribution of photon energies in the cavity will deviate from that of a black body. This yields Kirchhoff's law : α λ = ε λ {\displaystyle \alpha _{\lambda }=\varepsilon _{\lambda }} By

1392-686: Is the intensity of black-body radiation at wavelength λ {\displaystyle \lambda } and temperature T {\displaystyle T} . Independent of the condition of thermal equilibrium, the emissivity of the wall is defined as the ratio of emitted energy to the amount that would be radiated if the wall were a perfect black body. The emitted energy is thus ε λ E b λ ( λ , T ) {\displaystyle \varepsilon _{\lambda }E_{b\lambda }(\lambda ,T)} where ε λ {\displaystyle \varepsilon _{\lambda }}

1450-414: Is then put a small piece of carbon. Without the small piece of carbon, there is no way for non-equilibrium radiation initially in the cavity to drift towards thermodynamic equilibrium. When the small piece of carbon is put in, it transduces amongst radiation frequencies so that the cavity radiation comes to thermodynamic equilibrium. For experimental purposes, a hole in a cavity can be devised to provide

1508-502: The Teller-Ulam design . The casing's purpose is to contain and focus the energy of the primary ( fission ) stage in order to implode the secondary ( fusion ) stage. Kirchhoff%27s law of thermal radiation In heat transfer , Kirchhoff's law of thermal radiation refers to wavelength-specific radiative emission and absorption by a material body in thermodynamic equilibrium , including radiative exchange equilibrium. It

1566-410: The emissivity : the ratio of the emissive power of the body to the emissive power of a black body of the same size and shape at the same fixed temperature. With this definition, Kirchhoff's law states, in simpler language: In some cases, emissive power and absorptivity may be defined to depend on angle, as described below. The condition of thermodynamic equilibrium is necessary in the statement, because

1624-427: The ultraviolet catastrophe . The correct form of the law was found by Max Planck in 1900, assuming quantized emission of radiation, and is termed Planck's law . This marks the advent of quantum mechanics . In a blackbody enclosure that contains electromagnetic radiation with a certain amount of energy at thermodynamic equilibrium, this " photon gas " will have a Planck distribution of energies. One may suppose

1682-445: The weak nuclear force is not invariant under T-symmetry alone; if weak interactions are present, reversible dynamics are still possible, but only if the operator π also reverses the signs of all the charges and the parity of the spatial co-ordinates ( C-symmetry and P-symmetry ). This reversibility of several linked properties is known as CPT symmetry . Thermodynamic processes can be reversible or irreversible , depending on

1740-498: The Planck constant). Then applying k B T = ( ∂ E S ) − 1 {\displaystyle k_{B}T=(\partial _{E}S)^{-1}} , Planck obtained the black body radiation law. Another argument that does not depend on the precise form of the entropy function, can be given as follows. Next, suppose we have a material that violates Kirchhoff's law when integrated, such that

1798-419: The above equations, the above averages α s u n {\displaystyle \alpha _{\mathrm {sun} }} and ε p a i n t {\displaystyle \varepsilon _{\mathrm {paint} }} are not generally equal to each other. The white paint will serve as a very good insulator against solar radiation, because it is very reflective of

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1856-420: The absorptivity at a certain incidence direction, for a certain frequency, of a certain polarization, is the same as the emissivity at the same direction, for the same frequency, of the same polarization. This is the principle of detailed balance. Before Kirchhoff's law was recognized, it had been experimentally established that a good absorber is a good emitter, and a poor absorber is a poor emitter. Naturally,

1914-769: The average emissivity is given by: ε p a i n t = ∫ 0 ∞ ε λ ( λ , T ) E b λ ( λ , T ) d λ ∫ 0 ∞ E b λ ( λ , T ) d λ {\displaystyle \varepsilon _{\mathrm {paint} }={\frac {\int _{0}^{\infty }\varepsilon _{\lambda }(\lambda ,T)E_{b\lambda }(\lambda ,T)\,d\lambda }{\int _{0}^{\infty }E_{b\lambda }(\lambda ,T)\,d\lambda }}} where I λ s u n {\displaystyle I_{\lambda \mathrm {sun} }}

1972-404: The capsule with D-T gas. The X-ray intensity around the capsule must be very symmetrical to avoid hydrodynamic instabilities during compression. Earlier designs had radiators at the ends of the hohlraum, but it proved difficult to maintain adequate X-ray symmetry with this geometry. By the end of the 1990s, target physicists developed a new family of designs in which the ion beams are absorbed in

2030-486: The cavity radiation will precisely obey Planck's law. In this sense, thermodynamic equilibrium cavity radiation may be regarded as thermodynamic equilibrium black-body radiation to which Kirchhoff's law applies exactly, though no perfectly black body in Kirchhoff's sense is present. A theoretical model considered by Planck consists of a cavity with perfectly reflecting walls, initially with no material contents, into which

2088-403: The change in entropy during the process. Note, however, that the fundamental laws that underlie the thermodynamic processes are all time-reversible (classical laws of motion and laws of electrodynamics), which means that on the microscopic level, if one were to keep track of all the particles and all the degrees of freedom, the many-body system processes are all reversible; However, such analysis

2146-416: The dimensionless coefficient of absorption (or the absorptivity) is the fraction of incident light (power) at each spectral frequency that is absorbed by the body when it is radiating and absorbing in thermodynamic equilibrium. In slightly different terms, the emissive power of an arbitrary opaque body of fixed size and shape at a definite temperature can be described by a dimensionless ratio, sometimes called

2204-414: The energy as X-rays , a process known as indirect drive. The advantage to this approach, compared to direct drive, is that high mode structures from the laser spot are smoothed out when the energy is re-radiated from the hohlraum walls. The disadvantage to this approach is that low mode asymmetries are harder to control. It is important to be able to control both high mode and low mode asymmetries to achieve

2262-441: The equality of emissivity and absorptivity often does not hold when the material of the body is not in thermodynamic equilibrium. Kirchhoff's law has another corollary: the emissivity cannot exceed one (because the absorptivity cannot, by conservation of energy ), so it is not possible to thermally radiate more energy than a black body, at equilibrium. In negative luminescence the angle and wavelength integrated absorption exceeds

2320-433: The first system. If the optical filter passed only that frequency band, then there would be a net transfer of photons, and their energy, from the second system to the first. This is in violation of the second law of thermodynamics, which requires that there can be no net transfer of heat between two bodies at the same temperature. In the second system, therefore, at each frequency, the walls must absorb and emit energy in such

2378-475: The fuel capsule explodes outward when ablated by the x-rays produced by the hohlraum wall upon irradiation by lasers. Due to Newton's third law, the inner portion of the fuel capsule implodes, causing the D-T fuel to be supercompressed, activating a fusion reaction. The radiation source (e.g., laser ) is pointed at the interior of the hohlraum rather than at the fuel capsule itself. The hohlraum absorbs and re-radiates

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2436-404: The hohlraum walls, so that X-rays are radiated from a large fraction of the solid angle surrounding the capsule. With a judicious choice of absorbing materials, this arrangement, referred to as a "distributed-radiator" target, gives better X-ray symmetry and target gain in simulations than earlier designs. The term hohlraum is also used to describe the casing of a thermonuclear bomb following

2494-399: The interface. In this sense the material of the opaque body is black to radiation that reaches it, while the whole phenomenon, including the interior and the interface, does not show perfect blackness. In Planck's model, perfectly black bodies, which he noted do not exist in nature, besides their opaque interior, have interfaces that are perfectly transmitting and non-reflective. The walls of

2552-410: The linear reciprocity of the wave equation , which states that the time reversed solution of a wave equation is also a solution to the wave equation since standard wave equations only contain even derivatives of the unknown variables. Thus, the wave equation is symmetrical under time reversal, so the time reversal of any valid solution is also a solution. This means that a wave's path through space

2610-543: The material absorbs more than it emits at ν 1 {\displaystyle \nu _{1}} , and conversely at ν 2 {\displaystyle \nu _{2}} . Now, place this material in one Hohlraum. It would spontaneously create a shift in the spectrum, making it higher at ν 2 {\displaystyle \nu _{2}} than at ν 1 {\displaystyle \nu _{1}} . However, this then allows us to tap from one Hohlraum with

2668-416: The material's emission; however, such systems are powered by an external source and are therefore not in thermodynamic equilibrium. Kirchhoff's law of thermal radiation has a refinement in that not only is thermal emissivity equal to absorptivity, it is equal in detail . Consider a leaf. It is a poor absorber of green light (around 470 nm), which is why it looks green. By the principle of detailed balance, it

2726-593: The operator equation: Any time-independent structures (e.g. critical points or attractors ) which the dynamics give rise to must therefore either be self-symmetrical or have symmetrical images under the involution π. In physics , the laws of motion of classical mechanics exhibit time reversibility, as long as the operator π reverses the conjugate momenta of all the particles of the system, i.e. p → − p {\displaystyle \mathbf {p} \rightarrow \mathbf {-p} } ( T-symmetry ). In quantum mechanical systems, however,

2784-434: The process are the same as the statistical properties for time-reversed data from the same process. In mathematics , a dynamical system is time-reversible if the forward evolution is one-to-one , so that for every state there exists a transformation (an involution ) π which gives a one-to-one mapping between the time-reversed evolution of any one state and the forward-time evolution of another corresponding state, given by

2842-424: The radiation that falls on them, right in an infinitely thin surface layer, with no reflection and no scattering. They emit radiation in perfect accord with Lambert's cosine law . Gustav Kirchhoff stated his law in several papers in 1859 and 1860, and then in 1862 in an appendix to his collected reprints of those and some related papers. Prior to Kirchhoff's studies, it was known that for total heat radiation,

2900-484: The ratio had not been explicitly considered in its own right as a function of wavelength and temperature. Kirchhoff's original contribution to the physics of thermal radiation was his postulate of a perfect black body radiating and absorbing thermal radiation in an enclosure opaque to thermal radiation and with walls that absorb at all wavelengths. Kirchhoff's perfect black body absorbs all the radiation that falls upon it. Every such black body emits from its surface with

2958-407: The ratio of emissive power to absorptive ratio was the same for all bodies emitting and absorbing thermal radiation in thermodynamic equilibrium. This means that a good absorber is a good emitter. Naturally, a good reflector is a poor absorber. For wavelength specificity, prior to Kirchhoff, the ratio was shown experimentally by Balfour Stewart to be the same for all bodies, but the universal value of

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3016-1103: The resonator from one Hohlraum and connect it to another. If the thermal equilibrium were different, then we have just transported energy from one to another, violating the second law. Therefore, the spectrum of all black bodies are identical at the same temperature. Using a heuristic of quantization, which he gleaned from Boltzmann, Planck argued that a resonator tuned to frequency ν {\displaystyle \nu } , with average energy E {\displaystyle E} , would contain entropy S ν = k B [ ( 1 + E h ν ) ln ⁡ ( 1 + E h ν ) − E h ν ln ⁡ E h ν ] {\displaystyle S_{\nu }=k_{B}\left[\left(1+{\frac {E}{h\nu }}\right)\ln \left(1+{\frac {E}{h\nu }}\right)-{\frac {E}{h\nu }}\ln {\frac {E}{h\nu }}\right]} for some constant h {\displaystyle h} (later termed

3074-705: The same for all sets of time increments {  τ s  }, for s = 1, ...,  k for any k : A univariate stationary Gaussian process is time-reversible. Markov processes can only be reversible if their stationary distributions have the property of detailed balance : Kolmogorov's criterion defines the condition for a Markov chain or continuous-time Markov chain to be time-reversible. Time reversal of numerous classes of stochastic processes has been studied, including Lévy processes , stochastic networks ( Kelly's lemma ), birth and death processes , Markov chains , and piecewise deterministic Markov processes . Time reversal method works based on

3132-407: The second law of thermodynamics predicates that the entropy of the entire universe must not decrease, not because the probability of that is zero, but because it is so unlikely that it is a statistical impossibility for all practical considerations (see Crooks fluctuation theorem ). A stochastic process is time-reversible if the joint probabilities of the forward and reverse state sequences are

3190-402: The solar radiation, and although it therefore emits poorly in the solar band, its temperature will be around room temperature, and it will emit whatever radiation it has absorbed in the infrared, where its emission coefficient is high. Historically, Planck derived the black body radiation law and detailed balance according to a classical thermodynamic argument, with a single heuristic step, which

3248-405: The study of heat radiation. Planck analyzed such bodies with the approximation that they be considered topologically to have an interior and to share an interface . They share the interface with their contiguous medium, which may be rarefied material such as air, or transparent material, through which observations can be made. The interface is not a material body and can neither emit nor absorb. It

3306-402: The total coefficient of absorption is not equal to the coefficient of emission at a certain T {\displaystyle T} , then if the material at temperature T {\displaystyle T} is placed into a Hohlraum at temperature T {\displaystyle T} , it would spontaneously emit more than it absorbs, or conversely, thus spontaneously creating

3364-440: Was later interpreted as a quantization hypothesis. In Planck's set up, he started with a large Hohlraum at a fixed temperature T {\displaystyle T} . At thermal equilibrium, the Hohlraum is filled with a distribution of EM waves at thermal equilibrium with the walls of the Hohlraum. Next, he considered connecting the Hohlraum to a single small resonator , such as Hertzian resonators. The resonator reaches

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