151 research outputs found
Charged Particle Motion in a Highly Ionized Plasma
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\kappa_D/ 4\pi T is small, where \kappa_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[C g^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
Fokker-Planck equation describes the longitudinal straggling and 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.Comment: Comments: Published in Phys. Rep. 410/4 (2005) 237; RevTeX, 111
Pages, 17 Figures; Transcription error corrected in temperature equilibration
rate (3.61) and (12.44) which replaces \gamma-2 by \gamma-
Rigorous theory of nuclear fusion rates in a plasma
Real-time thermal field theory is used to reveal the structure of plasma
corrections to nuclear reactions. Previous results are recovered in a fashion
that clarifies their nature, and new extensions are made. Brown and Yaffe have
introduced the methods of effective quantum field theory into plasma physics.
They are used here to treat the interesting limiting case of dilute but very
highly charged particles reacting in a dilute, one-component plasma. The highly
charged particles are very strongly coupled to this background plasma. The
effective field theory proves that this mean field solution plus the one-loop
term dominate; higher loop corrections are negligible even though the problem
involves strong coupling. Such analytic results for very strong coupling are
rarely available, and they can serve as benchmarks for testing computer models.Comment: 4 pages and 2 figures, presented at SCCS 2005, June 20-25, Moscow,
Russi
Charged Particle Motion in a Plasma: Electron-Ion Energy Partition
A charged particle traversing a plasma loses its energy to both plasma
electrons and ions. We compute the energy partition, the fractions
and E_\smI/E_0 of the initial energy of this `impurity particle' that
are deposited into the electrons and ions when it has slowed down into an
equilibrium distribution that we shall determine. We use a well-defined
Fokker-Planck equation for the phase space distribution of the charged impurity
particles in a weakly to moderately coupled plasma. The Fokker-Planck equation
holds to first sub-leading order in the dimensionless plasma coupling constant,
which means we compute to order (leading) and (sub-leading) in the
plasma density . Previously, the order terms had been estimated, not
calculated. Since the charged particle does not come to rest, the energy loss
obtained by an integration of a has an ambiguity of order of the plasma
temperature. Our Fokker-Planck formulation provides an unambiguous, precise
definition of the energy fractions. For equal electron and ion temperatures, we
find that our precise results agree well with a fit obtained by Fraley,
Linnebur, Mason, and Morse. The case with differing electron and ion
temperatures, a case of great importance for nuclear fusion, will be
investigated in detail in the present paper. The energy partitions for this
general case, partitions that have not been obtained before, will be presented.
We find that now the proper solution of the Fokker-Planck equation yields a
quasi-static equilibrium distribution to which fast particles relax that has
neither the electron nor the ion temperature. This "schizophrenic" final
ensemble of slowed particles gives a new mechanism to bring the electron and
ion temperatures together. The rate at which this new mechanism brings the
electrons and ions in the plasma into thermal equilibrium will be computed.Comment: Improved abstract, introduction, and conclusion
Analysis of Dislocation Mechanism for Melting of Elements: Pressure Dependence
In the framework of melting as a dislocation-mediated phase transition we
derive an equation for the pressure dependence of the melting temperatures of
the elements valid up to pressures of order their ambient bulk moduli. Melting
curves are calculated for Al, Mg, Ni, Pb, the iron group (Fe, Ru, Os), the
chromium group (Cr, Mo, W), the copper group (Cu, Ag, Au), noble gases (Ne, Ar,
Kr, Xe, Rn), and six actinides (Am, Cm, Np, Pa, Th, U). These calculated
melting curves are in good agreement with existing data. We also discuss the
apparent equivalence of our melting relation and the Lindemann criterion, and
the lack of the rigorous proof of their equivalence. We show that the would-be
mathematical equivalence of both formulas must manifest itself in a new
relation between the Gr\"{u}neisen constant, bulk and shear moduli, and the
pressure derivative of the shear modulus.Comment: 19 pages, LaTeX, 9 eps figure
Dislocation-Mediated Melting: The One-Component Plasma Limit
The melting parameter of a classical one-component plasma is
estimated using a relation between melting temperature, density, shear modulus,
and crystal coordination number that follows from our model of
dislocation-mediated melting. We obtain in good agreement
with the results of numerous Monte-Carlo calculations.Comment: 8 pages, LaTe
- …