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Abbreviations
- c:
-
velocity of light
- me :
-
electron mass
- mi :
-
mass of an ion
- β:
-
ratio of the electron mass to the ion mass
- t:
-
time
- e:
-
charge of the electron
- ω0i :
-
plasma frequency
- H:
-
magnetic field strength
- ω∼ :
-
frequency of the magnetic field at the plasma-vacuum boundary
- VA :
-
Alfvén velocity
- V:
-
volume in units of N −10
- N:
-
particle density
- ξ:
-
Lagrange coordinate of the particles in units of c/ω0i
- τ:
-
time in units of c/(ω0iVA)
- νeff :
-
effective collision frequency
- χ:
-
collision frequency in units of ωeH
- up :
-
mass velocity of the particles
- u:
-
mass velocity of the particles in units of VA
- x0 :
-
Euler coordinate of the particles in units of c/ω0i,
- ωiH :
-
cyclotron frequency of the ions
- ωeH:
-
cyclotron frequency of the electrons
- ω:
-
frequency of the magnetic field in units of ωiH
- ξmax :
-
coordinate of the plane of symmetry in units of c/ω0i
- ux,y,z :
-
projections of the mass velocity of the particles on the x, y, and z axes in units of VA
- hy,z :
-
projections of the magnetic field on the y and z axes in units of H0
- Δ:
-
width of the wave front in units of c/ω0i
- Δux :
-
width of the particle velocity front in units of c/ω0i
- δN :
-
width of the particle density front in units of c/ω0i
- h⊥ :
-
ransverse magnetic field in units of H0
Literature cited
P. G. Saffman, “Propagation of a solitary wave along a magnetic field in a cold collision-free plasma,” J. Fluid Mech.,11, Pt. 1 (1961).
B. A. Tverskoi, “Uniform self-similar waves propagating along a magnetic field in a plasma,” Zh. Éksper. Teor. Fiz.,42, 3 (1962).
A. D. Pataraya, “Propagation of nonlinear plasma oscillations along a magnetic field,” Zh. Tekh. Fiz.,32, 2 (1962).
Yu. A. Berezin, “Cylindrical waves propagating perpendicular to a magnetic field in a rarefied plasma,” Zh. Prikl. Mat. Tekh. Fiz., No. 1 (1966).
V. D. Shafranov, “Electromagnetic waves in a plasma,” in: Reviews of Plasma Physics, Vol. 3, Consultants Bureau (1967).
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Additional information
Translated from Zhurnal Prikladnoi Mechaniki i Tekhnicheskoi Fiziki, No. 1, pp. 141–143, January–February, 1971.
The authors thank R. Z. Sagdeev for useful discussions.
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Berezin, Y.A., Dudnikova, G.I. Nonstationary waves propagating along a magnetic field in a plasma. J Appl Mech Tech Phys 12, 128–130 (1971). https://doi.org/10.1007/BF00853995
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DOI: https://doi.org/10.1007/BF00853995