Tadas K. Nakamura

Statistical Mechanics of a Collisionless System Based on the Maximum Entropy Principle

The statistical equilibrium state of a collisionless system has been derived based on the maximum entropy principle. The result shows that the equilibrium distribution function is a Gaussian distribution in the nondegenerate limit. This result contradicts the Lynden-Bell statistics, which predict a superposition of Fermi distributions as the equilibrium distribution. It is shown that the Lynden-Bell statistics are equivalent to maximizing the entropy calculated from the probability of particle transition, whereas the probability of particle existence should be used to obtain the correct answer.

Parallel electric field of a mirror kinetic Alfvén wave

It has been shown that an Alfven wave can create an electric field along the magnetic field line due to mirror effect. In a converging magnetic field, mobility of electrons is restricted by the mirror force and a parallel electric field must exist to carry a field aligned current associated with Alfven waves. The parallel electric field created by this mechanism can be much larger than that of a kinetic or inertial Alfven wave when the wave frequency is low enough. The essential mechanism of parallel electric field generation is reduced to the static mirror model in the limit where the wave frequency vanishes.

Three Views of a Secret in Relativistic Thermodynamics

It has been shown three different views in relativistic thermodynamics can be derived from the basic formulation proposed by van Kampen and Israel. The way to decompose energy-momentum into work and heat is not uniquely determined; the different choices result in different views. Also the definition of three dimensional volume causes ambiguity of thermodynamical quantities. The present paper shows various theories are obtained depending on the choice of these two factors. Subject Index: 070

Relativistic equilibrium distribution by relative entropy maximization

The equilibrium state of a relativistic gas has been calculated based on the maximum entropy principle. Though the relativistic equilibrium state was long believed to be the Juttner distribution, a number of papers have been published in recent years proposing alternative equilibrium states. Some of these papers do not pay enough attention to the covariance of distribution functions, resulting in confusion in equilibrium states. Starting from a fully covariant expression, it has been shown in the present paper that the Juttner distribution is the maximum entropy state if we assume the Lorentz symmetry.

Covariant thermodynamics of an object with finite volume

Abstract A covariant way to define the relativistic entropy of a finite object has been proposed. The energy–momentum in a finite volume is not a covariant physical entity because of the relativity of simultaneity. A way to correctly handle this situation is introduced and applied to the calculation of entropy. The result together with van Kampen–Israel theory gives simple and self-consistent relativistic thermodynamics.

Lorentz transform of black-body radiation temperature

The Lorentz transform of black-body radiation has been investigated from the viewpoint of relativistic statistical mechanics. The result shows that the well-known expression with the directional temperature can be derived based on the inverse-temperature four-vector. The directional temperature in the past literature was the result of mathematical manipulation and its physical meaning is not clear. The inverse-temperature four-vector has, in contrast, clear meaning to understand relativistic thermodynamical processes.

Thermodynamics of extended bodies in special relativity

Relativistic thermodynamics is generalized to accommodate four-dimensional rotation in a flat spacetime. An extended body can be in equilibrium when each of its elements moves along a Killing flow. There are three types of basic Killing flows in a flat spacetime, each of which corresponds to translational motion, spatial rotation, and constant linear acceleration; spatial rotation and constant linear acceleration are regarded as four-dimensional rotation. Translational motion has been mainly investigated in the past literature of relativistic thermodynamics. Thermodynamics of the other two is derived in the present paper.

Relativistic Statistical Mechanics with Angular Momentum

The equilibrium distribution function of a relativistic ideal gas has been derived to include the effect of angular momentum. The result agrees with the one obtained from kinetic theory, and consistent with relativistic thermodynamics. The role of angular momentum becomes transparent in this derivation, and the equilibrium distribution can be generalized to accommodate the effect of intrinsic angular momentum. The results here is for a flat spacetime, however, same approach can be applied to static curved spacetimes.

An analytical expression for electron drift resonances with lower hybrid waves in a curved magnetic field

Abstract Two new methods for linear kinetic calculation have been applied to the lower hybrid drift instability (LHDI) to obtain an analytical dispersion relation. One method is to carry out the orbit integration in the place of the conventional “method of characteristics”. With this method we found that the resonance condition of the LHDI becomes a quadratic function of the parallel and perpendicular (to ambient magnetic field) velocities. To carry out the velocity integration for this quadratic resonance condition, we apply the second method, a rational approximation to the distribution function, to obtain a result expressed with elementary functions.

Interpretation of pulse-like electric field distortions observed by Exos D satellite

The 32-Hz electric field data measured by the electric field detector EFD-P on board the EXOS D satellite show pulse-like distortions (PLDs) in nearly 10% of 1000 paths selected at random from April 1989 to June 1990. The purpose of the present paper is to analyze these distortions as a basis for future measurements of the parallel electric field in space. The PLDs are observed at altitudes higher than about 3000 km, with a typical duration of a few tens of minutes. Comparing with data obtained by other detectors on board EXOS D, it is suggested that the necessary conditions for the appearance of the distortions are (1) low plasma density, which implies a large Debye sphere around the spacecraft, (2) low ambient electron flux, which is necessary to keep the spacecraft potential high enough to attract photoelectrons from the probes, (3) small angle between the magnetic field and the wire probe, which makes the photoelectrons emitted from the probe accessible to the satellite, and (4) asymmetry in the photoelectron current from a pair of probes. When all four of these conditions are satisfied simultaneously, then the photoelectrons emitted from the probes reach the spacecraft body and produce spurious current flows in the measurement circuit to generate PLDs. A generation mechanism proposed here can explain well all the observed properties of PLDs.