Quasi-Linear Theory of Plasma Oscillations in an Electric Field

1963 ◽  
Vol 6 (8) ◽  
pp. 1196 ◽  
Author(s):  
Peter D. Noerdlinger
Keyword(s):  
Electric Field ◽  
Linear Theory ◽  
Plasma Oscillations

Damping of Plasma Oscillations in the Linear Theory

1961 ◽  
Vol 4 (11) ◽  
pp. 1387 ◽  
Author(s):  
John N. Hayes
Keyword(s):  
Linear Theory ◽  
Plasma Oscillations

A new derivation of quasilinear theory

1970 ◽  
Vol 4 (3) ◽  
pp. 595-602 ◽  
Author(s):  
J. P. Klozenberg ◽  
Ira B. Bernstein
Keyword(s):  
Electric Field ◽  
Wave Interactions ◽  
Quasilinear Theory ◽  
Plasma Oscillations ◽  
Field Spectrum ◽  
Individual Wave ◽  
The Individual

A new derivation of quasilinear theory for plasma oscillations is given, subject to the neglect of wave-wave interactions. The theory, which applies equally to damping and growing waves, requires that the individual wave resonances be narrow and the electric field spectrum sufficiently broad.

Electric Field Dependent Plasma Oscillations in Semiconductors

1970 ◽  
Vol 40 (1) ◽  
pp. 221-226 ◽  
Author(s):  
B. S. Krishnamurthy ◽  
V. V. Paranjape
Keyword(s):  
Electric Field ◽  
Plasma Oscillations ◽  
Field Dependent

Higher order approximations in the theory of longitudinal plasma oscillations

1967 ◽  
Vol 1 (4) ◽  
pp. 483-497 ◽  
Author(s):  
F. Einaudi ◽  
W. I. Axford
Keyword(s):  
Distribution Function ◽  
Electric Field ◽  
Linear Theory ◽  
Asymptotic Series ◽  
Finite Amplitude ◽  
Single Wave ◽  
Background Distribution ◽  
Damping Rate ◽  
Linear Behaviour ◽  
Longitudinal Plasma

The non-linear behaviour of one-dimensional electrostatic oscillations in a homogeneous, unbounded, collisionless and fully ionized plasma is considered for the case in which a single wave of small, but finite amplitude is excited initially. The Vlasov–Poisson equations are solved using the method of strained co-ordinates in which the independent variable t, the electric field and the distribution function are expanded in the form of asymptotic series, the terms of which are founded by an iterative procedure. An ordering parameter e is introduced, which is proportional to the initial amplitude of the electric field given by linear theory. Differential equations are derived which can be solved sequentially to obtain uniformly valid solutions to all orders in ε. Solutions are given to second order and applied to the case in which the background distribution function is Maxwellian. It is found that the changes in the real and imaginary part of the frequency are small in comparison to the values obtained in the linear theory; that the free-streaming terms decay exponentially in time with a damping rate proportional to ε2, in contrast with the linear theory where they are Un- damped; and that the analysis allows us to calculate the changes in the background distribution function for large time, resulting from particle-wave interactions.

Electric field gradient effects in an anti-plane circular inclusion in polarized ceramics

2006 ◽  
Vol 462 (2076) ◽  
pp. 3511-3522 ◽  
Author(s):  
J.S Yang ◽  
H.G Zhou ◽  
J.Y Li
Keyword(s):  
Exact Solution ◽  
Electric Field ◽  
Electric Field Gradient ◽  
Field Gradient ◽  
Linear Theory ◽  
Material Properties ◽  
Circular Inclusion ◽  
Effective Material Properties ◽  
Gradient Effects ◽  
Properties Of Composites

We analyse electric field gradient (or quadrupole) effects in the anti-plane problem of a small, circular inclusion in polarized ceramics. An exact solution is obtained. The solutions show that, different from the classical inclusion solution from the linear theory of piezoelectricity, the electric field in the inclusion is no longer uniform. This has implications in field concentration and strength considerations and the prediction of effective material properties of composites.

scholarly journals PAIR PRODUCTION IN A STRONG ELECTRIC FIELD: AN INITIAL VALUE PROBLEM IN QUANTUM FIELD THEORY

1993 ◽  
Vol 02 (02) ◽  
pp. 333-380 ◽  
Author(s):  
Y. KLUGER ◽  
J.M. EISENBERG ◽  
B. SVETITSKY
Keyword(s):  
Field Theory ◽  
Electric Field ◽  
Initial Value Problem ◽  
Particle Creation ◽  
Mean Field Approximation ◽  
Time Behavior ◽  
Initial Value ◽  
Plasma Oscillations ◽  
Physical Features ◽  
Creation Rate

We review recent achievements in the solution of the initial-value problem for quantum backreaction in scalar and spinor QED. The problem is formulated and solved in the semiclassical mean-field approximation for a homogeneous, time-dependent electric field. Our primary motivation in examining backreaction has to do with applications to theoretical models of production of the quark-gluon plasma though we here address practicable solutions for backreaction in general. We review the application of the method of adiabatic regularization to the Klein-Gordon and Dirac fields in order to renormalize the expectation value of the current and derive a finite coupled set of ordinary differential equations for the time evolution of the system. Three time scales are involved in the problem and therefore caution is needed to achieve numerical stability for this system. Several physical features like plasma oscillations and plateaus in the current appear in the solution. From the plateau of the electric current one can estimate the number of pairs before the onset of plasma oscillations, while the plasma oscillations themselves yield the number of particles from the plasma frequency. We compare the field-theory solution to a simple model based on a relativistic Boltzmann-Vlasov equation with a particle production source term inferred from the Schwinger particle creation rate and a Pauli-blocking (or Bose-enhancement) factor. This model reproduces very well the time behavior of the electric field and the creation rate of charged pairs of the semiclassical calculation. It therefore provides a simple intuitive understanding of the nature of the solution since nearly all the physical features can be expressed in terms of the classical distribution function.

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