Charged particle motion in a highly ionized plasma

Abstract

A recently introduced method utilizing dimensional continuation is employed to compute the energy loss rate for a non-relativistic particle moving through a highly ionized plasma. No restriction is made on the charge, mass, or speed of this particle. It is, however, assumed that the plasma is not strongly coupled in the sense that the dimensionless plasma coupling parameter g = e 2 κ D /4πT is small, where κ D is the Debye wave number of the plasma. To leading and next-to-leading order in this coupling, dE/dx is of the generic form g 2 ln[Cg 2 ]. The precise numerical coefficient out in front of the logarithm is well known. We compute the constant C under the logarithm exactly for arbitrary particle speeds. Our exact results differ from approximations given in the literature. The differences are in the range of 20% for cases relevant to inertial confinement fusion experiments. The same method is also employed to compute the rate of momentum loss for a projectile moving in a plasma, and the rate at which two plasmas at different temperatures come into thermal equilibrium. Again these calculations are done precisely to the order given above. The loss rates of energy and momentum uniquely define a Fokker-Planck equation that describes particle motion in the plasma. The coefficients determined in this way are thus well-defined, contain no arbitrary parameters or cutoffs, and are accurate to the order described. This FokkerPlanck equation describes the straggling -the spreading in the longitudinal position of a group of particles with a common initial velocity and positionand the transverse diffusion of a beam of particles. It should be emphasized that our work does not involve a model, but rather it is a precisely defined evaluation of the leading terms in a well-defined perturbation theory.

Measurements of Ion Stopping Around the Bragg Peak in High-Energy-Density Plasmas

“…The Brown-Preston-Singleton (BPS) [4] and the LiPetrasso (LP) stopping [5] formalisms were used to model the data. The BPS formalism includes a Coulomb logarithm in the weakly coupled limit, which is derived using the dimensional continuation method, and the LP stopping formalism is derived from a Fokker-Planck collision operator that uses an ad hoc Coulomb logarithm.…”

“…Over the last decades, ion stopping in weakly coupled to strongly coupled HEDP has been subject to extensive analytical and numerical studies [2][3][4][5][6][7][8][9][10], but only a limited set of experimental data exists to validate these theories. Most previous experiments also used only one type of ion with relatively high initial energy, in plasmas with n e < 10 23 cm −3 and T e < 60 eV [11][12][13][14][15][16][17][18][19][20][21].…”

Molecular dynamics studies of electron-ion temperature equilibration in hydrogen plasmas within the coupled-mode regime

“…Recent work on T -equilibration has involved both kinetic theory of various types [4][5][6][7][8], and MD simulations with like-charges and the pure Coulomb interaction [8,9] as well as opposite-charge simulations with quantum statistical potentials (QSPs) to mock up the effects of quantum diffraction [10][11][12][13][14]. All but a few of these studies [7,11,14] confined themselves to pure hydrogen (or the proton-positron system [8,9]).…”

Emergence of kinetic behavior in streaming ultracold neutral plasmas

“…Away from the initial gap, the streams move into regions of cold ions that are strongly coupled, which gives greater interest to such a measurement [48][49][50][51]. With sharper density features in the initial plasma, it may also be possible to excite and study shock waves [45,55].…”

“…One expects a greater penetration length for higher T e (0) because the Coulomb collision cross section decreases with collision velocity, σ ∝ 1/v 4 . From these measurements, it should also be possible to estimate the stopping power of electrons and strongly coupled ions in an ultracold plasma for a penetrating ion stream [48][49][50][51].…”