Self-Focusing Streams

Bennett, Willard H.

doi:10.1103/physrev.98.1584

Cited by 125 publications

(38 citation statements)

References 14 publications

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“…** This result is a little surprising, because it follows from what we said earlier that the plasma torus should actually more closely mimic a cylindrical caricature of a star, and the specific heat of a ''cylindrical maximum-entropy star'' (29) and its plasma physical clone, Bennett's cylindrical plasma beam (30,31), is nonnegative! The existence of a maximum-entropy plasma torus with negative specific heat therefore is a truly nontrivial fact.…”

mentioning

confidence: 82%

“…For all W(n) Ͻ E 1 down to W(n) ϭ Ϫ0.5 W • , where we terminated the computation, the plasma torus has higher entropy than the toroidal plasma sheet at the same effective energy. By asymptotic analysis we found that also for W(n) n Ϫϱ, and by continuity for W(n) Ͻ Ͻ ϪW • , the maximum-entropy configuration consists of a highly concentrated plasma torus that, in rescaled coordinates centered at the density maximum, converges to Bennett's cylindrical plasma beam (30,31) as W(n) n Ϫϱ. On the basis of this evidence we surmise that the plasma torus has maximum entropy for all W(n) Ͻ E 1 , implying its S stability in the class of rotationally invariant plasma with effective energy W(n) Ͻ E 1 and current I.…”

Section: Explicitlymentioning

confidence: 94%

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Negative specific heat of a magnetically self-confined plasma torus

Kiessling

Neukirch

2003

Proc. Natl. Acad. Sci. U.S.A.

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It is shown that the thermodynamic maximum-entropy principle predicts negative specific heat for a stationary, magnetically selfconfined current-carrying plasma torus. Implications for the magnetic self-confinement of fusion plasma are considered.T he goal of the controlled thermonuclear fusion program is to make the energy source that powers our sun available to human society. Deep in our sun's interior, favorable conditions for the quasistationary nuclear burning of the solar plasma prevail as a result of the immense gravitational self-forces that keep this huge accumulation of matter together. Because gravitational self-confinement is not operative at the reactor and laboratory scale, alternate means of confinement have to be used to achieve sufficiently high plasma densities and temperatures in a reactor. In the perhaps most prominent stationary fusion-reactor scheme, the tokamak, strong electric ring currents are induced in an electrically neutral plasma to achieve axisymmetric magnetic self-confinement in a rotationally invariant toroidal vessel T. In a torus with a sufficiently large major axis, such a magnetic self-confinement mimics gravitational self-confinement on account of the Biot-Savart law, according to which in a system of parallel current filaments all filaments attract each other magnetically with the same force law as would be the case gravitationally in a system of parallel mass filaments. What makes the magnetic forces more attractive (in the double sense of this phrase) than gravity for laboratory purposes is their very much bigger coupling constant [Ϸ10 40 v 2 ͞c 2 for two electrons moving on parallel trajectories with speed v as measured in the laboratory; note that the even stronger (v 2 ͞c 2 is replaced by 1) electrostatic repulsive forces between the same two electrons are very effectively screened in a neutral plasma and are traditionally neglected to a good approximation]. Of course, the analogy does not extend to all aspects of plasma selfconfinement. In particular, the solenoidal-vectorial character of stationary current densities necessitates the toroidal topology of magnetic self-confinement, whereas gravity not only allows but manifestly prefers spherical confinement over toroidal. Unfortunately, axisymmetric toroidal magnetic selfconfinement is not known for its stability either. Although major efforts are devoted to the stabilization of the plasma configuration, a vast reservoir of instabilities capable of destroying the confinement has dramatically slowed down the development of an operating tokamak fusion reactor.Matters are not exactly helped by the fact that our theoretical understanding of the physics on the various space-time scales that govern magnetic plasma confinement is still quite incomplete. In particular, although the solenoidal character of the magnetic induction together with the axisymmetry and stationarity of the law of momentum balance tell us that the poloidal magnetic f lux function ⌿ and the toroidal current density j must satisfy some local functional r...

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mentioning

confidence: 82%

Section: Explicitlymentioning

confidence: 94%

Negative specific heat of a magnetically self-confined plasma torus

Kiessling

Neukirch

2003

Proc. Natl. Acad. Sci. U.S.A.

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“…Such complications vanish for electron-positron plasmas, or quark-gluon plasmas. In this appendix, we will summarize the self-pinching solutions to the collisionless Vlasov equations found by Bennett [47] in the simplifying situation where opposite charges have the same mass. This includes the ultrarelativistic limit, where particle masses are ignored.…”

Section: Appendix D: Lattice Version Of Toy Modelmentioning

confidence: 99%

“…Finally, there is only one filament left in their simulation volume, and the plasma stabilizes in this configuration. This final configuration is clearly anisotropic and corresponds to an equilibrium solution to the Vlasov equations originally found by Bennett in 1934 [47], which we review for the ultra-relativistic case (where it is simpler) in Appendix E. Because of the parity-noninvariance of the initial state, the simulations of Honda et al could end up with a parity-noninvariant final state, described by the Bennett self-pinching filament. It is possible, in contrast, that generic parity-invariant initial conditions may lead to isotropization through collisionless processes, as suggested by the results of Califano et al…”

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confidence: 99%

Abelianization of QCD plasma instabilities

2004

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QCD plasma instabilities appear to play an important role in the equilibration of quark-gluon plasmas in heavy-ion collisions in the theoretical limit of weak coupling (i.e. asymptotically high energy). It is important to understand what non-linear physics eventually stops the exponential growth of unstable modes. It is already known that the initial growth of plasma instabilities in QCD closely parallels that in QED. However, once the unstable modes of the gauge-fields grow large enough for non-Abelian interactions between them to become important, one might guess that the dynamics of QCD plasma instabilities and QED plasma instabilities become very different. In this paper, we give suggestive arguments that non-Abelian self-interactions between the unstable modes are ineffective at stopping instability growth, and that the growing non-Abelian gauge fields become approximately Abelian after a certain stage in their growth. This in turn suggests that understanding the development of QCD plasma instabilities in the non-linear regime may have close parallels to similar processes in traditional plasma physics. We conjecture that the physics of collisionless plasma instabilities in SU(2) and SU(3) gauge theory becomes equivalent, respectively, to (i) traditional plasma physics, which is U(1) gauge theory, and (ii) plasma physics of U(1)×U(1) gauge theory.

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“…Previously, the relation was examined only numerically and it is the purpose of [2] to provide an approximate analytical expression for this relation valid for tokamaks, showing explicitly the dependence on the fueling parameters. The relation [3] implies a constraint on the thermal-energy content which cannot be violated, whatever the energy transport present and the plasma heating used. It should be noted that a different relation [4,5] has been derived.…”

Section: Introductionmentioning

confidence: 99%

Relationship between normalized thermal energy and conductivity for cylindrical tokamak geometry

Asif¹

2010

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Self-Focusing Streams

Cited by 125 publications

References 14 publications

Negative specific heat of a magnetically self-confined plasma torus

Negative specific heat of a magnetically self-confined plasma torus

Abelianization of QCD plasma instabilities

Relationship between normalized thermal energy and conductivity for cylindrical tokamak geometry

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