Adjustment of the electric charge and current in pulsar magnetospheres

📝 Abstract

We present a simple numerical model of the plasma flow within the open field line tube in the pulsar magnetosphere. We study how the plasma screens the rotationally induced electric field and maintains the electric current demanded by the global structure of the magnetosphere. We show that even though bulk of the plasma moves outwards with relativistic velocities, a small fraction of particles is continuously redirected back forming reverse plasma flows. The density and composition (positrons or electrons, or both) of these reverse flows are determined by the distribution of the Goldreich-Julian charge density along the tube and by the global magnetospheric current. These reverse flows could significantly affect the process of the pair plasma production in the polar cap accelerator. Our simulations also show that formation of the reverse flows is accompanied by the generation of long wavelength plasma oscillations, which could be converted, via the induced scattering on the bulk plasma flow, into the observed radio emission.

💡 Analysis

We present a simple numerical model of the plasma flow within the open field line tube in the pulsar magnetosphere. We study how the plasma screens the rotationally induced electric field and maintains the electric current demanded by the global structure of the magnetosphere. We show that even though bulk of the plasma moves outwards with relativistic velocities, a small fraction of particles is continuously redirected back forming reverse plasma flows. The density and composition (positrons or electrons, or both) of these reverse flows are determined by the distribution of the Goldreich-Julian charge density along the tube and by the global magnetospheric current. These reverse flows could significantly affect the process of the pair plasma production in the polar cap accelerator. Our simulations also show that formation of the reverse flows is accompanied by the generation of long wavelength plasma oscillations, which could be converted, via the induced scattering on the bulk plasma flow, into the observed radio emission.

📄 Content

arXiv:0904.2446v1 [astro-ph.HE] 16 Apr 2009 Adjustment of the electric charge and current in pulsar magnetospheres Yuri Lyubarsky Physics Department, Ben-Gurion University, P.O.B. 653, Beer-Sheva 84105, Israel ABSTRACT We present a simple numerical model of the plasma flow within the open field line tube in the pulsar magnetosphere. We study how the plasma screens the rotationally induced electric field and maintains the electric current demanded by the global structure of the magnetosphere. We show that even though bulk of the plasma moves outwards with relativistic velocities, a small fraction of particles is continuously redirected back forming reverse plasma flows. The density and composition (positrons or electrons, or both) of these reverse flows are determined by the distribution of the Goldreich-Julian charge density along the tube and by the global magnetospheric current. These reverse flows could significantly affect the process of the pair plasma production in the polar cap accelerator. Our simulations also show that formation of the reverse flows is accompanied by the generation of long wavelength plasma oscillations, which could be converted, via the induced scattering on the bulk plasma flow, into the observed radio emission. Subject headings: plasmas–(stars:) pulsars: general 1. Introduction The pulsar activity is believed to be associated with the generation of relativistic electron-positron plasma near the magnetic polar caps. This plasma flows along the open field line tube and eventually escapes from the magnetosphere forming a relativistic pulsar wind. Well within the light cylinder, the plasma currents do not distort significantly star’s magnetic field therefore in the frame corotating with the star, the plasma just moves along the axis of the rotating static dipole. An important point is that this motion could by no means be considered as free streaming because the basic electrodynamics dictates the charge and current densities at each point of the flow. First of all the charge density in the plasma should be equal to the local Goldreich-Julian charge density ρGJ = −Ω· B 2πc ; (1) – 2 – where B is the local magnetic field, Ωthe angular velocity of the neutron star. This condition is a generalization of the standard condition of the quasi-neutrality: deviation of the local charge density from ρGJ results in a longitudinal electric field, which redistributes the charges to establish ρ = ρGJ. The necessary field is weak in the sense that the corresponding potential is small as compared with the total rotationally induced potential; this is because the energy of the secondary plasma particles is small as compared with the total potential. Scharlemann (1974) and Cheng & Ruderman (1977) noted that in the plasma flow along the curved magnetic field lines, some difference should be maintained between the velocities of the electrons and positrons. The condition ρ = ρGJ implies n+ −n−∝B cos θ, where n± are the number density of positrons and electrons, correspondingly, θ the angle between the pulsar rotation axis and the magnetic field. Continuity of the particle flow implies n±V ± ∝ B, where V ± are the average velocities of the positrons and electrons, correspondingly. One sees that the average particle velocities should vary along a curved magnetic field line in accordance with the variation of θ. In a highly relativistic flow, V ± are close to c therefore even a small variation of θ implies a significant variation of the Lorentz factor of the positrons and electrons. Since the energy spread of the secondary particles is large, the electric field, which ensures the adjustment of the charge density, easily shifts the low-energy tail of the distribution function to the negative-momentum domain thereby forming a return particle flux (Lyubarskij 1992; Lyubarskii 1993a). Therefore one can expect counterstreaming plasma flows in the open field line tube. If the charge density in the flow is adjusted via sending ”extra” charges backwards, an electric current appears in the flow. However, the electric current is not a free parameter, which could be adjusted to maintain the necessary distribution of local charges. The current in the open field line tube is dictated by the global structure of the magnetosphere. The magnetic field lines are bent backwards with respect to the rotation direction in order to allow the plasma to stream along them at a velocity smaller than the speed of light even though the rotation velocity becomes superluminal beyond the light cylinder. The current should be distributed such that the necessary magnetic field is maintained (formally, the current along any magnetic field line is determined from the condition of the smooth transition of the flow through the light cylinder (Ingraham 1973; Contopoulos et al. 1999; Timokhin 2006)). Generally the current required by the global structure of the magnetosphere is not matched with the current established in the course of the charge density adjustment. This would resu

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