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Interaction of charged-particle beams with plasma

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Abbreviations

ω0 = √4πn 0 e 2/m :

Langmuir frequency of plasma electrons

ω oi = √4πn 0 e 2/M :

Langmuir frequency of plasma ions

Ω :

frequency

ω H :

electron Larmor frequency

ΩH :

Larmor ion frequency

δ = imω:

growth rate

δk :

growth rate for a wave characterized by wave vector k

Δω :

width of a resonance curve δ(Reω)

Vph :

phase velocity of a wave in the beam direction

k3 =ω/Vph :

projection of the wave vector in the beam direction

k∥ :

projection of the wave vector along fixed magnetic field

kℒ :

projection of the wave vector perpendicular to fixed magnetic field

k:

wave number

Imk:

spatial growth rate

V0 :

ordered beam velocity

v0 :

velocity of ordered motion in direction perpendicular to fixed magnetic field

VTe,i :

thermal velocity of electrons or ions

Vdr :

drift velocity

VA :

Al'fven velocity

n0 :

plasma density

n+ :

ion background density

n− :

density of electrons not trapped by wave

N:

number of particles in a bunch

n1 :

beam density

Tei :

electron temperature or ion temperature (given in degrees in tables)

θ 0 = kTe :

plasma electron temperature at t = 0 (herek is the Boltzmann constant)

θ ∥ andθ ℒ :

temperature of beam electrons parallel and perpendicular to the direction of beam motion, respectively

ΔΘ Λ :

change in transverse beam temperature

E0 :

fixed electric field

Ek :

amplitude of the wave corresponding to a given wave vector k

Emax :

field intensity at which stream breakup starts in the plasma

E:

electric field intensity

E e −1.5·10−8 n 0/T e v/cm:

critical electric field

Pℒ, P∥:

momenta transverse to and along magnetic field, respectively

θ :

angle between fixed magnetic field and direction of wave propagation

σ:

conductivity

nj(ω):

refractive index

Γ:

gamma function

λD :

Debye radius

ɛ :

particle energy

f :

distribution function

S:

flux of runaway electrons

a:

radius of plasma column

λ:

wavelength in vacuum

μ = m/M:

ratio of electron mass to ion mass

ri :

ion Larmor radius

L∥, Lℒ :

geometric dimensions of the system

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Fainberg, Y.B. Interaction of charged-particle beams with plasma. The Soviet Journal of Atomic Energy 11, 958–979 (1962). https://doi.org/10.1007/BF01473684

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