Abstract
The Weibel instability and the induced magnetic field are of great importance for both astrophysics and inertial confinement fusion. Because of the stochasticity of this magnetic field, its main wavelength and mean strength, which are key characteristics of the Weibel instability, are still unobtainable experimentally. In this paper, a theoretical model based on the autocorrelation tensor shows that in proton radiography of the Weibel-instability-induced magnetic field, the proton flux density on the detection plane can be related to the energy spectrum of the magnetic field. It allows us to extract the main wavelength and mean strength of the two-dimensionally isotropic and stochastic magnetic field directly from proton radiography for the first time. Numerical calculations are conducted to verify our theory and show good consistency between pre-set values and the results extracted from proton radiography.
Highlights
The Weibel instability, which is mainly characterized as being able to generate strong magnetic fields, is of great significance for a range of scenarios in plasma physics, and has been studied for many decades since it was first proposed[1,2,3,4]
We demonstrate for the first time that the mean strength and main spatial wavelength of the Weibel-instability-generated magnetic field can be inferred by means of proton radiography
For Weibel instability driven by electron thermal anisotropy, mostly investigated with an expanding plasma in the interaction of a laser pulse with a solid target, the magnetic field duration after saturation can reach the range of several tens of picoseconds, which is large enough to neglect the influence introduced by the probe pulse duration[15]
Summary
The Weibel instability, which is mainly characterized as being able to generate strong magnetic fields, is of great significance for a range of scenarios in plasma physics, and has been studied for many decades since it was first proposed[1,2,3,4]. In proton radiography of three-dimensionally isotropic and stochastic magnetic field turbulence, the mean strength and the main spatial wavelength of the magnetic turbulence can be inferred by extracting the energy spectrum of the magnetic energy EB(k) from the detected proton flux distribution[19,20,21]. It has been verified by numerical demonstrations and used to evidence dynamo amplification of magnetic fields in a turbulent plasma[22]. Numerical calculations based on ray tracing methods are conducted to verify our theory
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