The Diffusion and Thermalization of an Electron Cloud Injected into an Afterglow Plasma

1971 ◽  
Vol 49 (9) ◽  
pp. 1124-1136
Author(s):  
H. W. H. Van Andel
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Steady State ◽  
Boltzmann Equation ◽  
Axial Magnetic Field ◽  
Electron Cloud ◽  
Steady State Distribution ◽  
State Distribution ◽  
Account Electron ◽  
Afterglow Plasma

The steady state distribution function for a suprathermal electron cloud injected into a cylindrical plasma is found as a function of position and velocity by solving the Boltzmann equation numerically in the Fokker–Planck approximation with an added term taking into account electron-neutral collisions. The injection is assumed to take place at one end of the cylinder, and an axial magnetic field is assumed present. A number of representative solutions are given for various choices of the parameters of the problem.

Slowly propagating instabilities in plasmas with Margenau-Davydov electron distribution function

1980 ◽  
Vol 24 (3) ◽  
pp. 503-514 ◽  
Author(s):  
V. J. Žigman ◽  
B. S. Milić
Keyword(s):  
Distribution Function ◽  
Steady State ◽  
Absolute Stability ◽  
Electron Distribution ◽  
Electron Distribution Function ◽  
Electron Drift ◽  
Steady State Distribution ◽  
State Distribution ◽  
Weakly Ionized ◽  
Weakly Ionized Plasma

The properties of certain wave modes excited in a weakly ionized plasma placed in an external d.c. electric field are analyzed from the standpoint of the linearized kinetic equation, the electron steady-state distribution function being taken in the form of the extended Margenau–Davydov and, in particular, Druyvesteinian. The presence of absolute stability cones formed by certain propagation directions is found. The corresponding critical values of the electron drift, destabilizing each of the modes considered, is also evaluated for a plasma with a Druyvesteinian distribution.

A note on the waiting time in M[X]/G/1 queueing systems with a removable server

2004 ◽  
Vol 41 (1) ◽  
pp. 287-291
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Distribution Function ◽  
Steady State ◽  
Waiting Time ◽  
Queueing Systems ◽  
Stieltjes Transform ◽  
Steady State Distribution ◽  
State Distribution ◽  
Removable Server ◽  
Inactive Phase ◽  
Bulk Arrival

For the M[X]/G/1 queueing model with a general exhaustive-service vacation policy, it has been proved that the Laplace-Stieltjes transform (LST) of the steady-state distribution function of the waiting time of a customer arriving while the server is active is the product of the corresponding LST in the bulk arrival model with unremovable server and another LST. The expression given for the latter, however, is valid only under the assumption that the number of groups arriving in an inactive phase is independent of the sizes of the groups. We here give an expression which holds in the general case. For the N-policy case, we also give an expression for the LST of the steady-state distribution function of the waiting time of a customer arriving while the server is inactive.

The effects of thermal motion of neutrals on the non-potential instabilities in a weakly ionized sodium plasma

1982 ◽  
Vol 28 (1) ◽  
pp. 177-184 ◽  
Author(s):  
V. J. Žigman ◽  
B. S. Milić
Keyword(s):  
Distribution Function ◽  
Steady State ◽  
Cross Section ◽  
Thermal Motion ◽  
Moderate Intensity ◽  
Experimental Measurements ◽  
Steady State Distribution ◽  
State Distribution ◽  
Weakly Ionized ◽  
Sodium Plasma

The results of recent experimental measurements of the differential cross-section for elastic scattering of electrons on sodium atoms were used to evaluate the electron steady-state distribution function in a weakly ionized, uniform and non-magnetized sodium plasma placed in a d.c. electric field. The field was assumed to be of moderate intensity, so that the thermal motion of the neutrals had to be taken into account in the evaluation of the distribution function. The resulting ‘modified Druyvesteinian function’ was applied to study the non-potential instabilities arising from the presence of the field in this particular plasma. Threshold drifts for both very slow and slow modes were obtained and the conditions for the onset of instabilities were discussed. It is shown that the thermal motion of the neutrals affects both critical drifts and the angles of propagation.

A note on the waiting time in M[X]/G/1 queueing systems with a removable server

2004 ◽  
Vol 41 (01) ◽  
pp. 287-291
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Distribution Function ◽  
Steady State ◽  
Waiting Time ◽  
Queueing Systems ◽  
Stieltjes Transform ◽  
Steady State Distribution ◽  
State Distribution ◽  
Removable Server ◽  
Inactive Phase ◽  
Bulk Arrival

For the M[X]/G/1 queueing model with a general exhaustive-service vacation policy, it has been proved that the Laplace-Stieltjes transform (LST) of the steady-state distribution function of the waiting time of a customer arriving while the server is active is the product of the corresponding LST in the bulk arrival model with unremovable server and another LST. The expression given for the latter, however, is valid only under the assumption that the number of groups arriving in an inactive phase is independent of the sizes of the groups. We here give an expression which holds in the general case. For the N-policy case, we also give an expression for the LST of the steady-state distribution function of the waiting time of a customer arriving while the server is inactive.

Transport by weak electrostatic density drift fluctuations

1983 ◽  
Vol 30 (1) ◽  
pp. 153-168
Author(s):  
J. J. Sanderson ◽  
S. Peter Gary
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
Steady State ◽  
Uniform Magnetic Field ◽  
Distribution Functions ◽  
Lower Hybrid ◽  
Steady State Distribution ◽  
State Distribution ◽  
Particle Exchange ◽  
Vlasov Plasma

Expressions are derived for transport by weak electrostatic microfluctuations driven unstable by a density gradient perpendicular to a uniform magnetic field in a Vlasov plasma. These expressions, which are evaluated for the universal and lower-hybrid density drift instabilities, provide improved physical interpretations for various wave-particle exchange frequencies previously reported. It is demonstrated that wave-particle effects generally reduce the free energy driving these instabilities, and that some forms of steady-state distribution functions are inappropriate for nonlinear theory.

Sign in / Sign up

Export Citation Format

Share Document