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Chapter: 4 Atomic and nuclear physics
    Section: 4.4 Free electrons and ions in gases
        SubSection: 4.4.2 Electron mobility

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4.4.2 Electron mobility

Free electrons have a velocity which depends upon their energy. In the absence of an electric or magnetic field the electron energy approaches that of the thermal agitation energy of the gas atoms given by Maxwell, 3 kT/2. When an electric field is applied the electrons steadily drift in the field direction and because they lose only a small fraction of their energy in elastic collisions with gas atoms or molecules they rapidly gain energy until they start to undergo inelastic collisions. A single mobility value cannot be given (see ionic mobility) and the drift velocity as a function of E/N or E/p is normally found in the literature. For very low E/N, the drift velocity is proportional to E/N. At larger E/N values this relation is no longer valid as the drift velocity increases more rapidly than the linear relationship. Impurities, especially with the noble gases, are again of importance. The presence of very small quantities of a secondary gas which has a lower excitation or ionization potential than the principal gas can have a large effect on the electron properties. Electrons can be removed either by electron attachment to form negative ions, which because of their mass are effectively immobile compared to electrons or by recombination with a positive ion. They can reappear by electron detachment or by various ionization processes. Electrons can be characterized by their drift velocity, diffusion coefficient and by their ability to cause excitation or ionization of the gas atoms with which they collide.

The effect of a magnetic field is to change the trajectory of electrons—for high magnetic fields and long path lengths the effect can be very significant (Palladino and Sadoulet, 1975).

The theoretical basis for calculating drift velocities and diffusion coefficients using Boltzmann transport equations and the data for electron collision cross sections is now well established, for example see Va’vra (1992), so that values for many gas mixtures can be computed provided the basic data is available.

The table below is compiled mainly from Pack, Voshall and Phelps (1962) and McDaniel (1964).

Revised data for Ar/CH4 and data for Ar/CF4, Ar/C2H2 is from Christophorou et al. (1979), Ar/CO2 data from Nagy (1960), CF4 data from Va’vra (1992) and He/CF4 data from Schmidt (1992).

E/p values can be converted to Townsends by applying 1 Td = 0.266 V m N−1.


Drift velocity/(103 m s−1)

Gas

Field strength per unit pressure (E/p)/(V m N−1)

 

0.075

0.15

0.3

   0.45

0.6

0.75

1.5

3

4.5

6

7.5

15


H2    .    .    .    .    .


3.1


5   


6.8

   
  8.0


9.2


10     


15


23


30


36


42


70

He  .    .    .    .    .

2.7

4   

6   

7

8.5

9.6

15

36

 

 

 

 

N2  .    .    .    .    .

3.1

3.9

5   

6

7    

8    

14

22

30

36

43

80

Ne .    .    .    .    .

4    

5   

7   

10    

12     

16     

26

52

 

 

 

 

Ar  .    .    .    .    .

2.3

 2.7

3.2

  3.5

3.9

4.1

     6.2

13

30

 

 

  

Kr  .    .    .    .    .

1.5

1.8

2.1

  2.4

2.5

3.1

 

 

 

 

 

 

Xe  .    .    .    .    .

1.0

1.2

1.4

  1.6

1.7

1.8

 

 

 

 

 

 

CO2    .    .    .    .

   0.56

1.1

2.3

  3.4

4.6

 5.7

11

33

66

94

109    

137    

CO      .    .    .    .

4.8

6.5

9.4

11   

13     

14    

17

20

25

28

29

 

BF3 .    .    .    .    .

  0.13

  0.25

0.5

    0.75

1.0

 1.3

     2.5

    5.0

    7.5

10

   12.5

25

Air  .    .    .    .    .

3.5

5   

8   

  9.3

11     

12   

17

26

34

43

51

88

CH4     .    .    .    .

8   

24    

60     

80   

95     

100     

100   

 

 

 

 

 

CF4     .    .    .    .

30    

51   

74     

87   

96     

101     

117   

140  

141  

129   

116   

95

Ar/CH4    .    .    .

49    

55   

45     

36    

32     

30   

26

24

 

 

 

 

Ar/N2       .    .    .

4  

6

9   

13     

16.8

19.3

   27.3

 

 

 

 

 

Ar/C2H2   .    .    .

  14.3   

  27.3

44.3

49.3

48.3

45.8

  45.2

 

 

 

 

 

Ar/CF4     .    .    .

34   

63

100      

120     

120     

111      

  66   

 

 

 

 

 

He/CF4     .    .    .

 6   

  10.8

19.2

25.8

31.4

36    

 

 

 

 

 

 

3He/CO2   .    .    . 

    0.30

  0.56

    0.99

  1.4

  1.7

 2.0

     2.5

 

  

 

 

 

Ar/CO  .    .    .

  5.0

10.6

26.5

37.5

43   

42   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


    All binary mixtures are 90%/10% by volume.

J.W. Leake

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