28pB03
電子縮退プラズマ中の電子-イオン温度緩和率
Electron-ion temperature equilibration rate in electron degenerate plasmas
杉田昂平1、中尾安幸1、城﨑知至2
Kohei Sugita1, Yasuyuki Nakao1, and Tomoyuki Johzaki2
1

九大院工、2広大院工Kyushu Univ., 2Hiroshima Univ.

1

2. ModelThe equilibration of electron and ion temperature(Te , Ti ) via collisions is often described bydTe  ei Te  Ti , (1)dtdTi
  ie Ti  Ti , (2)dtwhere the parameter ei (ie) is equal to the reciprocal ofthe relaxation time and have been evaluated using
various methods, for example, Brown, Preston, andSingleton (BPS) used the dimensional continuation
method [3-5]. However their formula does notincorporate real time variation of temperature anddetailed energy distribution of particles, therefore wesolved the equation for distribution function of ionscoexisting with degenerate electrons [8] and evaluatedie from the time variation of ion temperature in order toremove vagueness as many as possible.

3. Results and discussion
Supposing fully ionized deuterium plasmas atvarious temperature (Ti ≠Te) as the initial values andfixing the distribution function of electrons, we evaluatedthe parameter ie by fitting obtained time variation of ion
temperature to Eq.(2). Figure 1 presents the parameter ie
as a function of electron temperature at electron number
density ne = 1026 cm-3. The points are obtained from thetime variation of ion temperature and dashed curves arefrom BPS formula. The red points and curve are resultsin the case considering the effect of electron degeneracy
and the blue ones are obtained ignoring the degeneracy
effect. For comparison, we plotted the results from othermodels [2,6,7]. At this density, BPS formula is accurate

above 0.5 keV [4], and except its neighborhood, ourcalculation gives similar results as the BPS model. The
parameter ie decreases with temperature because thefrequency of electron-ion interaction decreases. In
addition, it can be seen that the electron degeneracy
slows temperature equilibration and this tendency
become more significant at lower temperature. This isbecause Pauli’s exclusion principle reduces thefrequency of electron-ion interaction in the degenerateregion.
However each result shown in Fig.1 does notinclude strongly coupling plasma effects, which areimportant below about 0.2 keV, and it becomes incorrect
at very low temperatures.
26-3

ne = 10 cm-1

The temperature equilibration between electrons
and ions in dense plasma is one of the most importantphenomena for inertial confinement fusion (ICF) [1], andthen its calculation model has been modified recent years[2-6]. The rate of electron-ion temperature relaxation isdetermined by the magnitude and frequency ofelectron-ion interaction and is affected by various
physical processes. In highly-compressed plasmas asrealized in ICF implosions, the effect of electron
degeneracy becomes non-negligible [3]. However thiseffect has not been discussed sufficiently yet and theevaluation based on more rigorous treatment is necessary.
Thus we evaluated the rate parameter of electron-ion
temperature relaxation from the time variation of detailedenergy distribution of ions coexisting with degenerateelectrons.

rate parameter ie [sec ]1. Introduction

1013101210111010_________________________
w/ degeneracy effectw/o degeneracy effectBPS (w/ degeneracy effect)
BPS (w/o degeneracy effect)[7]
Spitzer[2]
Lee and More
[6]
from molecular-dynamics simulations

0.1

1

10100

electron temperature [keV]

Fig. 1The electron-ion temperature equilibration rate at ne= 1026 cm-3. All calculations start from Ti = Te / 2 as
the initial value.

4. Conclusion
Evaluating the rate of electron-ion temperaturerelaxation from the time variation of ion temperature, wehave found that the electron degeneracy decreases it.
Besides, comparing our results and BPS ones, we could
confirm the accuracy of our and their models except atvery low temperatures.
References[1] B. Xu and S. X. Hu, Phys. Rev. E 84, 016408 (2011).
[2] Y. T. Lee and R. M. More, Phys. Fluids 27, 1273 (1984).
[3] L. S. Brown, et al., Phys. Rep. 401, 237 (2005).
[4] L. S. Brown, et al., Phys. Rev. E 76, 066404 (2007).
[5] L. S. Brown and R. L. Singleton, Jr., Phys. Rev. E 79,066407 (2009).
[6] G. Diomnte and J. Daligaut, Phys. Rev. Lett. 101, 135001 (2008).
[7] L. Spitzer, Jr., Physics of Fully Ionized Gases (Interscience,New York, 1962).
[8] K. Sugita, et al., accepted for publication in Plasma andFusion Research.