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BEAM INSTABILITIES30

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Name

Conditions

Saturation Mechanism

Electron- electron

Vd > Vej, j = 1,2

Electron trapping until Ve,' - Vd

Buneman

Vd > (M/m)1//3Vi, Vd > Ve

Electron trapping until

Ve - Vd

Beam-plasma

Vb > (np/nb)1/3Vb

Trapping of beam electrons

Weak beam- plasma

Vb < (np/nb)1/3Vb

Quasilinear or nonlinear (mode coupling)

Beam-plasma (hot-electron)

ve>vb> Vb

Quasilinear or nonlinear

Ion acoustic

Te > Ti, Vd > Cs

Quasilinear, ion tail form­ation, nonlinear scattering, or resonance broadening.

Anisotropic temperature (hydro)

Te± > 2Te||

Isotropization

Ion cyclotron

Vd > 20Vi (for

Te ~ T^)

Ion heating

Beam-cyclotron (hydro)

Vd > cs

Resonance broadening

Modified two- stream (hydro)

Vd < (1 + /3)1/2Va, Vd > cs

Trapping

Ion-ion (equal beams)

U < 2(1 + /3)1/2Va

Ion trapping

Ion-ion (equal beams)

Z7 < 2CS

Ion trapping

For nomenclature, see p. 50.

Name

Parameters of Most Unstable Mode

Growth Rate

Frequency

Wave Number

Group Velocity

Electron- electron

Buneman Beam-plasma

Weak beam- plasma

Beam-plasma (hot-electron)

Ion acoustic

Anisotropic temperature (hydro)

Ion cyclotron

Beam-cyclotron (hydro)

Modified two- stream (hydro)

Ion-ion (equal beams)

Ion-ion (equal beams)

— LtJe 2

/mX1/3 0.7 — t»je \Mj

1/3

o.7 n*

\ nn

nb (Vb

UJt

2np \Vb

f 1/2 Yi Up J vb

UJ,

■UJf

m M

1/2

UJo

0.1 Qi 0.7Qe

 

0AQH OAvi

0

ZmX1/3 0.4 — oje \Mj

uje

f nb\ 1//S 0.4 — toe

\nv J

UJe

Vb V,

UJi

UJe cos 6 rsj

1.2 Qi nQe

0.9Qh

0 0

UJe

0.9 —

Vd

UJe

Vd

ue

Vb

UJe

Vb

X

X

d

d

-1

r.

%

0.7A

1.7

1.2

-l d

Vd

Vh

U

UJi 1.2 —

U

0

2

-vd

3 2

Vb Vb

Cs

VeX

1 - 3*

^ Vd;

< cs 1

— Vd 2

For nomenclature, see p. 50.

In the preceding tables, subscripts e, i, d, 6, p stand for "electron," "ion," "drift," "beam," and "plasma," respectively. Thermal velocities are denoted by a bar. In addition, the following are used:

m

electron mass

re,ri

gyroradius

M

ion mass

/3

plasma/magnetic energy

V

velocity

 

density ratio

T

temperature

VA

Alfven speed

Tie 5 Tli

number density

^e 5

gyrofrequency

n

harmonic number

 

hybrid gyrofrequency,

Cs = (Te/M)X/2

ion sound speed

 

QH2 = ^e^i

UJe, UJi

plasma frequency

u

relative drift velocity of

\D

Debye length

 

two ion species

Авторы: 1379 А Б В Г Д Е З И Й К Л М Н О П Р С Т У Ф Х Ц Ч Ш Щ Э Ю Я

Книги: 1908 А Б В Г Д Е З И Й К Л М Н О П Р С Т У Ф Х Ц Ч Ш Щ Э Ю Я