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Register a new userAnalytic expressions for electron-ion temperature equilibration rates from the Lenard-Balescu equation
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In this work, we elucidate the mathematical structure of the integral that arises when computing the electron-ion temperature equilibration time for a homogeneous weakly-coupled plasma from the Lenard-Balescu equation. With some minor approximations, we derive an exact formula, requiring no input Coulomb logarithm, for the equilibration rate that is valid for moderate electron-ion temperature ratios and arbitrary electron degeneracy. For large temperature ratios, we derive the necessary correction to account for the coupled-mode effect, which can be evaluated very efficiently using ordinary Gaussian quadrature.
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In the mean-field regime, the evolution of a gas of $N$ interacting particles is governed in first approximation by a Vlasov type equation with a self-induced force field. This equation is conservative and describes return to equilibrium only in the very weak sense of Landau damping. However, the first correction to this approximation is given by the Lenard-Balescu operator, which dissipates entropy on the very long timescale $O(N)$. In this paper, we show how one can derive rigorously this correction on intermediate timescales (of order $O(N^r)$ for $r<1$), close to equilibrium.
The unshielded nature of gravity means that stellar systems are inherently inhomogeneous. As a result, stars do not move in straight lines. This obvious fact severely complicates the kinetic theory of stellar systems because position and velocity turn out to be poor coordinates with which to describe stellar orbits - instead, one must use angle-action variables. Moreover, the slow relaxation of star clusters and galaxies can be enhanced or suppressed by collective interactions (polarisation effects) involving many stars simultaneously. These collective effects are also present in plasmas; in that case, they are accounted for by the Balescu-Lenard (BL) equation, which is a kinetic equation in velocity space. Recently several authors have shown how to account for both inhomogeneity and collective effects in the kinetic theory of stellar systems by deriving an angle-action generalisation of the BL equation. Unfortunately their derivations are long and complicated, involving multiple coordinate transforms, contour integrals in the complex plane, and so on. On the other hand, Rostokers superposition principle allows one to pretend that a long-range interacting $N$-body system, such as a plasma or star cluster, consists merely of uncorrelated particles that are dressed by polarisation clouds. In this paper we use Rostokers principle to provide a simple, intuitive derivation of the BL equation for stellar systems which is much shorter than others in the literature. It also allows us to straightforwardly connect the BL picture of self-gravitating kinetics to the classical two-body relaxation theory of uncorrelated flybys pioneered by Chandrasekhar.
We demonstrate that the scaling properties of slab ion and electron temperature gradient driven turbulence may be derived by dimensional analysis of a drift kinetic system with one kinetic species. These properties have previously been observed in gyrokinetic simulations of turbulence in magnetic fusion devices.
Hamiltonian matrices appear in a variety or problems in physics and engineering, mostly related to the time evolution of linear dynamical systems as for instance in ion beam optics. The time evolution is given by symplectic transfer matrices which are the exponentials of the corresponding Hamiltonian matrices. We describe a method to compute analytic formulas for the matrix exponentials of Hamiltonian matrices of dimensions $4times 4$ and $6times 6$. The method is based on the Cayley-Hamilton theorem and the Faddeev-LeVerrier method to compute the coefficients of the characteristic polynomial. The presented method is extended to the solutions of $2,ntimes 2,n$-matrices when the roots of the characteristic polynomials are computed numerically. The main advantage of this method is a speedup for cases in which the exponential has to be computed for a number of different points in time or positions along the beamline.
Charges in cold, multiple-species, non-neutral plasmas separate radially by mass, forming centrifugally-separated states. Here, we report the first detailed measurements of such states in an electron-antiproton plasma, and the first observations of the separation dynamics in any centrifugally-separated system. While the observed equilibrium states are expected and in agreement with theory, the equilibration time is approximately constant over a wide range of parameters, a surprising and as yet unexplained result. Electron-antiproton plasmas play a crucial role in antihydrogen trapping experiments.
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