ANISOTROPIC ELECTRON DISTRIBUTION FUNCTIONS AND THE TRANSITION BETWEEN THE WEIBEL AND THE WHISTLER INSTABILITIES
F. Pegoraro, L. Palodhi, F. Califano
Physics Department Pisa University and CNISM, Pisa, Italy
Electron distribution functions that are anisotropic in phase space are a common feature of collisionless plasmas both in space and in the laboratory and the investigation of the processes through which these distributions relax is of primary interest. In fact, the free energy that is made available by the unbalance of the particle “temperatures” in the different directions can be transferred, depending on the plasma conditions, to quasistatic magnetic fields, to electromagnetic or electrostatic coherent structures or to particle acceleration.
The anisotropy of the electron distribution function in an unmagnetized plasma can give rise to
the onset of the well known Weibel instability which generates a quasistatic magnetic field.
If a magnetic field is already present in the plasma, the Weibel instability driven by the anisotropy
of the electron energy distribution turns into the so called whistler instability, in which case circularly
polarized whistler waves are generated by the relaxation of the electron distribution function.
Whistler waves are actually ubiquitous in plasmas and their generation has been extensively studied
in recent years in the laboratory. Whistler instabilities have been reported in space where bursts
of whistler mode magnetic noise are found to be present in the magnetosphere, close to the magnetopause
and are also a likely source of several different magnetospheric fluctuations including
plasmaspheric hiss and magnetospheric chorus.
In this presentation the transition between non resonant (Weibel-type) and resonant (whistler)
instabilities is investigated numerically in plasma configurations with an ambient magnetic field of
increasing amplitudes. The Vlasov-Maxwell system is solved in a configuration where the fields
have three components but depend only on one coordinate and on time. The nonlinear evolution of
these instabilities is shown to lead to the excitation of electromagnetic and electrostatic modes at
the first few harmonics of the plasma frequency and, in the case of a large ambient magnetic field,
to a long-wavelength, spatial modulation of the amplitude of the magnetic field generated by the
L. Palodhi, F. Califano, F. Pegoraro, Nonlinear Kinetic Development of the Weibel Instability and
the generation of electrostatic coherent structures, Plasma Physics and Controlled Fusion 51, 125006
L. Palodhi, F. Califano, F. Pegoraro, On the transition between the Weibel and the whistler instabilities,
Plasma Physics and Controlled Fusion 52 095007 (2010).