Beams and Beam Physics
5
FIGURE 1.2: Sketch of an early thermionic emission electron source.
(Reprinted with permission from J. R. Pierce, J. of Appl. Phys., 11:548,
1940 [57]. Copyright 1940, AIP Publishing LLC.)
The first of these processes is thermionic emission. By heating a piece
of metal to temperatures exceeding around 1000
◦ C, a small fraction of the
electrons will achieve energies exceeding the work function and can thus leave
the metal. This type of source is usually called the thermionic gun. Once
outside the metal, the electrons can be pulled away further by the application
of strong electric fields, the distribution of which is adjusted to achieve high
gradient and optimal focusing. An example of such a device is shown Fig. 1.2.
Here the number of electrons available is determined by the temperature of
the donor metal or cathode, and only those electrons in the tail of the FermiDirac distribution above the work function can be extracted. This process is
quantitatively described by the Richardson-Dushman equation
J =
4πemk
2
B
h 3
T
2 e
−W/kB T ,
(1.7)
where J is the current density, e is the charge, m is the mass, k B is the
Boltzmann constant, h is the Planck constant and T is the temperature of
the cathode. It is obtained from the third law of thermodynamics and characterizes an idealized situation of a sufficiently large piece of cathode material
to avoid quantum mechanical influences, and the absence of electric fields
influencing extraction.
In practice the extracted current is also greatly affected by any electric field
applied to the cathode. This is the result of the Coulomb repulsion among the
extracted electrons, where electrons extracted earlier can push those extracted
later back into the cathode. When the electric field at the surface vanishes, no
more electrons will be extracted. The relation between the maximum current
density and the applied electric field, for a parallel flat cathode and a matching
anode, is the Child-Langmuir Law
J =
4
9
0
2e
m
1/2 V
3/2
0
d 2 ,
(1.8)
5
FIGURE 1.2: Sketch of an early thermionic emission electron source.
(Reprinted with permission from J. R. Pierce, J. of Appl. Phys., 11:548,
1940 [57]. Copyright 1940, AIP Publishing LLC.)
The first of these processes is thermionic emission. By heating a piece
of metal to temperatures exceeding around 1000
◦ C, a small fraction of the
electrons will achieve energies exceeding the work function and can thus leave
the metal. This type of source is usually called the thermionic gun. Once
outside the metal, the electrons can be pulled away further by the application
of strong electric fields, the distribution of which is adjusted to achieve high
gradient and optimal focusing. An example of such a device is shown Fig. 1.2.
Here the number of electrons available is determined by the temperature of
the donor metal or cathode, and only those electrons in the tail of the FermiDirac distribution above the work function can be extracted. This process is
quantitatively described by the Richardson-Dushman equation
J =
4πemk
2
B
h 3
T
2 e
−W/kB T ,
(1.7)
where J is the current density, e is the charge, m is the mass, k B is the
Boltzmann constant, h is the Planck constant and T is the temperature of
the cathode. It is obtained from the third law of thermodynamics and characterizes an idealized situation of a sufficiently large piece of cathode material
to avoid quantum mechanical influences, and the absence of electric fields
influencing extraction.
In practice the extracted current is also greatly affected by any electric field
applied to the cathode. This is the result of the Coulomb repulsion among the
extracted electrons, where electrons extracted earlier can push those extracted
later back into the cathode. When the electric field at the surface vanishes, no
more electrons will be extracted. The relation between the maximum current
density and the applied electric field, for a parallel flat cathode and a matching
anode, is the Child-Langmuir Law
J =
4
9
0
2e
m
1/2 V
3/2
0
d 2 ,
(1.8)