Relativistic distribution functions and applications to electron beams

Wright, Thomas P.; Hadley, G. Ronald

doi:10.1103/physreva.12.686

Cited by 43 publications

(41 citation statements)

References 23 publications

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“…Inserting this into Equation (1), we find the Maxwell-Jüttner distribution (Jüttner 1911;Wright & Hadley 1975) where T is measured in the COM frame of the beam. These simple scalings of the perpendicular velocity dispersion and parallel velocity dispersions can be understood as a result of time dilation between two frames that are boosted relative to each other, giving one factor of g -1 .…”

Section: Distribution Function Of the Pair Beammentioning

confidence: 99%

THE LINEAR INSTABILITY OF DILUTE ULTRARELATIVISTIC e^± PAIR BEAMS

Chang

Broderick

Pfrommer

et al. 2016

ApJ

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The annihilation of TeV photons from extragalactic TeV sources and the extragalactic background light produces ultrarelativistic  e beams, which are subject to powerful plasma instabilities that sap their kinetic energy. Here we study the linear phase of the plasma instabilities that these pair beams drive. To this end, we calculate the linear growth rate of the beam-plasma and oblique instability in the electrostatic approximation in both the reactive and kinetic regimes, assuming a Maxwell-Jüttner distribution for the pair beam. We reproduce the well-known reactive and kinetic growth rates for both the beam-plasma and oblique mode. We demonstrate for the oblique instability that there is a broad spectrum of unstable modes that grow at the maximum rate for a wide range of beam temperatures and wave-vector orientations relative to the beam. We also delineate the conditions for applicability for the reactive and kinetic regimes and find that the beam-plasma mode transitions to the reactive regime at a lower Lorentz factor than the oblique mode due to a combination of their different scalings and the anisotropy of the velocity dispersions. Applying these results to the ultrarelativistic  e beams from TeV blazars, we confirm that these beams are unstable to both the kinetic oblique mode and the reactive beam-plasma mode. These results are important in understanding how powerful plasma instabilities may sap the energy of the ultrarelativistic  e beams as they propagate through intergalactic space.

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Section: Distribution Function Of the Pair Beammentioning

confidence: 99%

THE LINEAR INSTABILITY OF DILUTE ULTRARELATIVISTIC e^± PAIR BEAMS

Chang

Broderick

Pfrommer

et al. 2016

ApJ

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“…Usually these electrons are characterized by a distribution function f (E), which is often represented as a Maxwellian, or more simply an exponential slope. At high intensity a relativistic Maxwellian (Jüttner distribution) is used [36]. In the following we have used for simplicity exponential functions:…”

Section: Influence Of Target Heating On K α and Kβ Observablesmentioning

confidence: 99%

Effects of target heating on experiments usingKαandKβdiagnostics

et al. 2015

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We describe the impact of heating and ionization on emission from the target of Kα and Kβ radiation induced by the propagation of hot electrons generated by laser-matter interaction. We consider copper as a test case and, starting from basic principles, we calculate the changes in emission wavelength, ionization cross section, and fluorescence yield as Cu is progressively ionized. We have finally considered the more realistic case when hot electrons have a distribution of energies with average energies of 50 and 500 keV (representative respectively of "shock ignition" and of "fast ignition" experiments) and in which the ions are distributed according to ionization equilibrium. In addition, by confronting our theoretical calculations with existing data, we demonstrate that this study offers a generic theoretical background for temperature diagnostics in laser-plasma interactions.

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“…A variety of descriptions can be found in the literature, ranging from monokinetic (Bludman et al 1960, Pegoraro et al 1996 to Maxwellian-like (Yoon 1989 (Yoon & Davidson 1987, Silva et al 2002, Bret et al 2005, Cottrill et al 2008 and Kappa (Lazar et al 2008) distributions. However, in order to address potentially large (relativistic) thermal spreads, it appears convenient to model the beam-plasma system by means of drifting Maxwell-Jüttner distribution functions (Jüttner 1911, Wright & Hadley 1975 …”

Section: Main Instability Classes and Their Related Propertiesmentioning

confidence: 99%

Theory of fast electron transport for fast ignition

et al. 2014

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Abstract. Fast Ignition Inertial Confinement Fusion is a variant of inertial fusion in which DT fuel is first compressed to high density and then ignited by a relativistic electron beam generated by a fast (< 20 ps) ultra-intense laser pulse, which is usually brought in to the dense plasma via the inclusion of a re-entrant cone. The transport of this beam from the cone apex into the dense fuel is a critical part of this scheme, as it can strongly influence the overall energetics. Here we review progress in the theory and numerical simulation of fast electron transport in the context of Fast Ignition. Important aspects of the basic plasma physics, descriptions of the numerical methods used, a review of ignition-scale simulations, and a survey of schemes for controlling the propagation of fast electrons are included. Considerable progress has taken place in this area, but the development of a robust, high-gain FI 'point design' is still an ongoing challenge.

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Relativistic distribution functions and applications to electron beams

Cited by 43 publications

References 23 publications

THE LINEAR INSTABILITY OF DILUTE ULTRARELATIVISTIC e^± PAIR BEAMS

THE LINEAR INSTABILITY OF DILUTE ULTRARELATIVISTIC e^± PAIR BEAMS

Effects of target heating on experiments usingKαandKβdiagnostics

Theory of fast electron transport for fast ignition

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Relativistic distribution functions and applications to electron beams

Cited by 43 publications

References 23 publications

THE LINEAR INSTABILITY OF DILUTE ULTRARELATIVISTIC e± PAIR BEAMS

THE LINEAR INSTABILITY OF DILUTE ULTRARELATIVISTIC e± PAIR BEAMS

Effects of target heating on experiments usingKαandKβdiagnostics

Theory of fast electron transport for fast ignition

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Product

Resources

About

THE LINEAR INSTABILITY OF DILUTE ULTRARELATIVISTIC e^± PAIR BEAMS

THE LINEAR INSTABILITY OF DILUTE ULTRARELATIVISTIC e^± PAIR BEAMS