||One-dimensional plasma models exhibit some thermodynamic properties or ergodic behavior of real plasmas; of many-body systems, a one-dimensional plasma model, consisting of a number of identical charged sheets embedded in a uniform fixed neutralizing background, is such a representative one.|
Thermal relaxation is an evolution during which a thermodynamic system approaches to thermal equilibrium. If a system of identical one-dimensional particles takes into account only two-particle correlations, no thermal relaxation takes place. Rather, due to the long-range forces among the background and the sheets themselves, as the initial velocity of sheets is either square or quadratic, the velocity of sheets will relax to Maxwellian; the system will attain to thermal equilibrium.
The topics in this thesis:
1. Energy conservation in the numerical scheme
The program deals with the discretized time to solve the approximated traces of sheets; therefore, it is necessary to examine the influence of the period t of a time interval on the total energy per sheet. It turns out that the total energy per sheet is dependent on the cube of the time increment.
2. The ratio of the electric energy per sheet to the kinetic energy per sheet in thermal equilibrium
3. Time development of the 2 statistic constructed by the velocities of sheets
In addition to provide statistical evidence that the velocity distribution of sheets relaxes to Maxwellian, the chi-squared statistic measures the thermal relaxation time, decaying exponentially asymptotically.
4. The dependence of the thermal relaxation time R on nD
By use of the quadratic fitting, R seems to depend on the square of nD, and it is consistent with Dawson’s conclusion. With the power fitting, it is found that the exponent for the quadratic profile is closer to 2 than that for the square profile.
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