Kinetic simulations of electron–positron induced streaming instability in the context of gamma-ray halos around pulsars

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Volume 688 (August 2024)

A&A, 688 (2024) A134

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Table 1

Notations used in this work.

Quantity	Notation
Light speed, elementary charge	c, e
Frequency, wavenumber	ω, k
Magnetic field strength	B
Particle species	α (e, i, cr)
(electron, proton, CRs)
Mass, charge, momentum	m_α q_α, p_α
Lorentz factor	$γ_{α} = \sqrt{1 + {(p_{α} / m_{α} c)}^{2}}$ $\[\gamma_\alpha=\sqrt{1+\left(p_\alpha / m_\alpha c\right)^2}\]$
Gyrofrequency	$Ω_{α} = q_{α} B / γ_{α} m_{α} c = Ω_{c α} / γ_{α}$ $\[\Omega_\alpha=q_\alpha B / \gamma_\alpha m_\alpha c=\Omega_{c \alpha} / \gamma_\alpha\]$
Gyroradius	R_L,α = c/Ω_cα
Background density	n_i = n_e
Beam density	n_cr
Alfvén velocity	$V_{A} = B / \sqrt{4 π n_{i} m_{i}}$ $\[V_{\mathrm{A}}=B / \sqrt{4 \pi n_{\mathrm{i}} m_i}\]$
Drift velocity	V_D
Electron/ion temperature (background)	Te,i = θ_bg m_ec²/k_B
Electron plasma frequency	$ω_{p e} = \sqrt{4 π n_{e} e^{2} / m_{e}}$ $\[\omega_{\mathrm{pe}}=\sqrt{4 \pi n_{\mathrm{e}} e^2 / m_{\mathrm{e}}}\]$
Electron skin-depth	d_e = c/ω_pe

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