The electrons in the welding electron guns are emitted usually by a thermionic cathode, which supply the free electrons. The current density je at thermal electron emission from a cathode heated to temperature Tc is given by Richardson-Dushman equation:
je = A. Tc 2
exp(-kTc
e
) , (93)
where e
is the work function of the emitter (namely
is the potential of the surface gap of cathode material electrons in free electron observation), e is the elementary charge of an electron, k is the Boltzmann constant being equal to 1.38.10-23 J.deg-2 ; A is a constant, depending from the material of the cathode and construction of the electrodes . Theoretical value of A is 120 A/(cm2.K2)In a diode emitting system (simplest two-electrode construction in which emitted current can be generated) the current density je will be observed only in the case of enough big potential drop applied on the cathode /anode space. Observation of a saturation of the emitted current collected by the anode at various voltages and given Tc could be seen (Figure 46).; at lower voltages the current-voltage characteristics is controlled by Child - Langmuir law (exponent 3/2 law) as this is shown on Figure 46. The Figure 46-a is idealized case, and Figure 46b is the real observable current-voltage characteristics of a vacuum diode generator of electrons.
Figure 46a. I-V characteristics of an idealized vacuum diode; temperatures T3 >T2> T1
Figure 46b. I-V characteristics of a real vacuum diode
Figure 47. Current density vs. temperature of the cathode
To obtain desired high beam current density (or energy flow density) the current is emitted from cathodes obeying higher emission ability – as example Tungsten, Tantalum or LaB6 . The choice of that materials is done as compromise between the emitted current densities and evaporation rates at given temperature and low ion sputtering yield (see Figure
Design of High Brightness Welding Electron Guns and Characterization… 65
47 to Figure 49). These factors limited the life of the emitter. Properties of emitter material after heating of the emitter(changes of crystalline grains; selective evaporation and/or activation etc., and workability are also important at that choice. An attempt to compare mentioned emitter materials is shown in Table 11. Additionally metals able to be used as emitters are Rhenium and Niobium. Rhenium obeys a similar behavior as the Ta at higher temperatures.
Figure 48. Evaporation rate vs. current density of cathode
Table 11. Emission properties of cathode materials
Property Tungsten Tantalum Molybdenum LaB6
4.52 4.07 4.15 2.86 (2.36* )Tc[oC] 2300-2700 1950-2150 1800-2000 1000-1600
A[A/cm2.oC2] 60(70) 60(55) 55 73 (120*)
je [A/cm2] 1-10 0.1-0.5 0.00083at 1600 oC 1-50 Ion bombardment
stability
Very good poor good
Changes after heating
Becomes brittle
Remains soft Active surface
(improved emission at 1600 oC)
Workability poor good good Extremely poor
* data published in [39]
Figure 49. Relative ion sputtering yields of W and LaB6 (abscissa-time; ordinate-weight losses) From pure metals W is excellent as emitting ability and low erosion at ion bombardment.
Tantalum is deformable and better workability. Fabrication of filaments and spherical segments in the user place is easy to be realized from tantalum. For technological guns as emitter material often the choice is LaB6. Their not very high working temperature is advantage for a decrease of the heating power, but condensation of the evaporated or sputtered refractory metal on the emitter surface decreases its electron emission. As a result LaB6 emitters are not implemented in EB welding systems for joining refractory metals.
The real diode system is demonstrated voltage current characteristic, different than shown on Figure 46a (see Figure 46b). At values of voltage Ua≤0 there are currents (one can see region of initial currents, due to Maxwell distribution of the velocities of the emitted electrons). At big voltage values are observed so called Shottky effect at which the emission of electrons is controlled by decrease of e
due to the outer electric field.This is not auto-electron emission (at electrical field of order 108 - 109 V/m this is possible only on a tip – than the potential barrier is too narrow and tunneling transition of free electrons become possible; i.e. at auto-electron emission not need of emitter heating). Due to smooth transition between regions of ―3/2 law‖ and of ―saturation of thermo-emission current
‖ in the voltage-current characteristics (mainly as result of Shottky effect, but also due to the real roughness and to the non-uniformity of the emitter surface) the real characteristics of emission current not obey exactly the theoretical equation (93) for saturated emission current density.
Due to Shotky effect the equation (93) can be written as
je = A. Tc and initial velocity of emitted electrons V0 =0 can be written as:
j = (
Design of High Brightness Welding Electron Guns and Characterization… 67
Here d is measured in [cm] and j is calculated in [A/cm2]. This equation is exact for emission of mono-energetic particles which initial velocities are equal to zero. The space charge of emitted electrons significantly affects the potential distribution near the cathode surface and could produce a potential minimum in the vicinity of the emitter. The maximal emitted current, limited by space charge is that, which is limited by potential distribution drop between diode electrodes, leading that on the emitter plane the potential gradient (i.e.
electrical field) have zero value instead the uniform gradient of potentials between these two flat electrodes if the diode is situated in vacuum. In the case of emission of electrons with distributed initial velocities some electrons will be able to go to the anode at 0 or at stopping electrical field in front of the cathode. So a difference of the real emitted current take place.
The problem in the case in which the charged particles are emitted with Maxwell velocity distribution had been solved by Langmuir [25].
For evaluation of universal function of potential distribution in front of a cathode one can assume dimensionless coordinates. Let dimensionless potential is:
e kT
U U
c a
/
min
, (96)where Umin is the minimum of the potential. The dimensionless distance from the cathode can be written as:
) (
2 z z
min
. (97)Figure 50. Potential distribution in the case of limited by space charge electron beam are emitted with Maxwell distribution of velocities of the electrons. The function is given in dimensionless parameters potential vs. distances
(
)as they are defined in eq.(96) and eq.(97)There zmin is the distance between cathode and potential minimum;
is a function of current density j and emitter temperature Tc, given by equation2
The function
(
)is tabulated (and/or available in the form of approximations) for two regions
≤0 and
≥0 (distances before and after the potential minimum-see Figure 50).Current (limited by temperature), can be assumed as part of the maximal emitted current, evaluated by (95). If in the front of the cathode exists a stopping electrical field generated by a potential Ur due to the Maxwell velocity distribution of the emitted electrons, the current density is:
j=jsexp(eUr/kTc) . (99)
The electrons height of potential barrier is Uc-Ur and using (96) one can find:
j/js = exp(-
c) (100)and
c
ln(j/js). (101)Equation (9) is an initial condition. From
c and
(
)for negative values of
one canfind