Initial-value problem for plasma oscillations in a uniform magnetic field

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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Excitation of surface waves in magnetohydrodynamics

Journal of Plasma Physics ◽

10.1017/s0022377800014732 ◽

1990 ◽

Vol 43 (2) ◽

pp. 183-188 ◽

Cited By ~ 1

Author(s):

Bhimsen K. Shivamoggi

Keyword(s):

Magnetic Field ◽

Gravitational Field ◽

Asymptotic Behaviour ◽

Pressure Distribution ◽

Surface Waves ◽

Initial Value Problem ◽

Large Time ◽

Far Field ◽

Two Dimensional ◽

Initial Value

A study is made of the transient development of two-dimensional linearized surface waves generated by a localized steady pressure distribution on the interface between a uniformly streaming, semi-infinite, infinitely conducting plasma subjected to a gravitational field and the confining vacuum magnetic field. The linearized equations associated with an initial-value problem are used to obtain the large-time asymptotic behaviour of the disturbance in the far field.

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