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Unformatted text preview: )dy
−∞ The integral in the numerator is integrable by parts
+∞ +∞ 1
1
2
− ∫ − exp(− y 2 )dy
∫ y exp(− y ) y dy = − 2 exp(− y ) y
2
−∞
−∞ [ 2 [ = 1 +∞
2
∫ exp(− y )dy
2 −∞ Canceling the integrals we have
⎛ྎ 1
3 ⎞ྏ
⎜ྎ mAvth ⎟ྏ
4
⎠ྏ = 1 mv 2 = 1 kT
Eav = ⎝ྎ
th
Avth
4
2 Temperature • (in 3 D) Eav=3KT/2 • Since T and Eav are so closely related, it is customary in plasma physics to give temperatures in units of energy. • To avoid confusion on the number of dimensions involved it is not Eav but rather the energy corresponding to kT that is used to denote the temperature. • For kT = 1 eV = 1.6 × 10 19 J, we have T= 1.6 × 10 −19
1.38 ×10 − 23 = 11,600 Thus the conversion factor is 1 eV = 11,600 oK • By a 2 eV plasma we mean that kT = 2 eV, or Eav = 3 eV in (3D) Debye Length • DEBYE SHIELDING Debye L...
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 Winter '14

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