L = n o l3 D
From the values given (T =10 6 K, and n = 10 10 /m3)
L = 2.9 x 10 8
N = 4p n o l3 D / 3
N = (4p)(9.2 x 10 6 ) / 3 = 1.2 x 10 9
2)For the solar atmosphere, first find the Debye length:
l D,s =[kT s / 4p Z s2 n s e2 ] 1/2
l D,s =[kT s / 4p n s e2 ] 1/2
l D,s =
[(1.38 x 10-23 (10 4 K) (8.85 x 10 -12 F/m) / (4p) (10 20/m3) e2 ] ½
3) For the laser fusion plasma we have for the Debye length:
lD , =
[(1.38 x 10-23 )(10 7 K) (8.85 x 10 -12 F/m) / (4p) (10 29/m3) e2 ] ½
[(1.38 x 10-23 )(10 7 K) (8.85 x 10 -12 F/m) / (4p) (10 29/m3) e2 ] ½
l D,s = 1.9 x 10 - 10 m
For the tail of Earth’s magnetosphere we have for the Debye length:
l D,s =
[(1.38 x 10-23 (10 7 K) (8.85 x 10 -12 F/m) / (4p) (10 6/m3) e2 ] ½
l D,s = 61.6 m
L = n o l3 D =
( 10 29 /m3) (1.9 x 10 - 10 m) 3
( 10 29 /m3) (1.9 x 10 - 10 m) 3
L = 0.74
N = 4p n o l3 D / 3 = 3
For the tail of Earth’s magnetosphere we have for the plasma parameter:
L = ( 10 6 /m3) (61.6 m) 3
L = 2.3 x 10 11
The number of particles in the Debye sphere:
N = 4p n o l3 D / 3 = 9.7 x 10 11
The values L, N are vastly larger for the tail of Earth’s magnetosphere
4)Can a plasma with n o = 10 6 /m3 be maintained at an electron temperature of 100K? (Hint: Calculate the density limit using the plasma parameter).
For these numbers the plasma parameter is:
And the Debye length is:
l D =10 0.84 (ÖT/ Ön) =
10 0.84 (Ö100K / Ö(10 6 /m3) = 0.069 m
= 3.0 x 10 9
N = 4p (3.0 x 10 9 ) / 3 = 1.2 x 10 10
5) In the limit 1/N << 1 and 1/N ® 0 we say a plasma is “collisionless”. Do any of the plasmas cited in the previous problems qualify as collisionless?
The values 1/N for the given plasmas are as follows:
helium plasma: 1/N = 1/ 3.8 x 10 7 = 2.6 x 10 - 8
solar atmosphere: 1/N = 1/3.1 = 0.32
laser fusion plasma: 1/N = 1/3.1 = 0.32
tail of Earth’s magnetosphere: 1/N = 10 – 12
The values 1/N show that only the helium and magnetospheric plasmas can be considered as collisionless.
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