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Kinetic cyclotron and synchrotron maser instabilities: Radio emission processes by direct amplification of radiation

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Abstract

This article reviews the theory of the kinetic (cyclotron an synchroton) maser instabilities. The subject has been extensively developed in recent years by many authors, who have been incited by the research of the auroral kilometric radiation and other applications. The maser mechanism is appealing because it is simple and efficient, and can lead to direct amplification of radiation. Two types of electron distribution functions have been investigated so far. These are the loss-cone and hollow-beam distributions which may exist pervasively in many regions within and beyond the solar system. It is likely that the maser instabilities can have many potentially important applications to numerous radio emission processes observed in astrophysical research.

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Abbreviations

F e :

The unperturbed distribution function of energetic electrons

ne=n o+n e :

Total electron density

n 0 :

Density of low energy background electrons

n e :

Density of energetic electrons

Subscripts ∥ and ⊥:

To indicate quantities and components in the directions parallel and perpendicular to the ambient magnetic field, respectively

B :

The ambient magnetic field

k :

Wavevector

v :

Velocity vector

u≡p/m e=y v :

Momentum per unit mass

m e :

Rest mass of an electron

\(\gamma = \left( {1 - \frac{{\upsilon ^2 }}{{c^2 }}} \right)^{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} 2}} \right. \kern-\nulldelimiterspace} 2}} = \left( {1 + \frac{{u^2 }}{{c^2 }}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \) :

The usual relativistic Lorentz factor

c :

The speed of light in vacuo

\(\Omega _e \left( {\frac{{|e|B_0 }}{{m_e c}}} \right)\) :

The electron cyclotron frequency

\(\omega '_{pe} \equiv \left( {\frac{{4\pi n_e e^2 }}{{m_e }}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \) :

The plasma frequency of the energetic electrons

\(\omega _{pe} \equiv \left( {\frac{{4\pi n_0 e^2 }}{{m_e }}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \) :

The plasma frequency of the background electrons. (Note: Readers may notice that, in some of the figures, ω pe is denoted as ω e )

n (or m):

A cyclotron harmonic number

w=w r+iw i :

A comples frequency

ω r :

The real part of ω

ω i :

The imaginary part of ω

\(N = \frac{{kc}}{{\omega _r }}\) :

The refractive index

θ :

The angle between k and B 0

J n (b) :

The Bessel function of order n

\(J'_n = \frac{{{\text{d}}J_n }}{{{\text{d}}b}}\) :

The derivate of J n with respect to b

\(b = \frac{{k_ \bot u_ \bot }}{{\Omega _e }}\) :

The argument of J n

α :

The dispersion of momentum per unit mass

δ[x]:

The delta function with argument x

φ :

The pitch angle of an electron, cos φ=u∥/=v∥/v

v e :

The thermal speed of the background thermal electrons

ê x ,ê y , and ê z :

Unit vectors in the x, y, and z directions

Λ :

Determinant of the matrix of Λ ij defined by Equation (4.2)

Λ 0 :

The portion of Λ associated with a background plasma

ω x :

The cutoff frequency of the RX-mode

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Wu, C.S. Kinetic cyclotron and synchrotron maser instabilities: Radio emission processes by direct amplification of radiation. Space Sci Rev 41, 215–298 (1985). https://doi.org/10.1007/BF00190653

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