The base way to measure angular distribution of beam electrons is use of two movable pin-hole plates and one collector electrode (Figure 3).
Pinhole method, shown on Figure 3, is difficult for direct use in case of characterization the powerful beams, due to destroying the first screen by beam heating. Note that as result of mention above analysis in ref. [18] one could evaluate, that about 106 sufficiently short sampling impulses and transfer rate twice higher than the maximum spectrum frequency can create adequate detailed image of the beam angular distributions. This means that for enough
Design of High Brightness Welding Electron Guns and Characterization… 39
adequate analysis a signal, collected from lot of measuring positions of both plates must be transferred and treated. This is too long for testing angular distribution in a production welding machine
More practical way for evaluating the beam angular distribution (and estimation of the beam emittance) for powerful electron beams, based on the multiple beam profile measurement, were proposed in [21-23]. In [21-23] emittance calculation by: a) the measurement of two beam profiles and a known focusing plane position or b)by three measurements of the beam current density profiles at three locations along the beam axis was proposed.
The emittance p and the standard deviations are related:
εp=C.ζx.ζx , (64)
where the coefficient C could be calculated as (see Figure 29):
C=[-2ln(1-p)]1/2. (65)
The relations between the emittance p and the product of x and x at a radial symmetrical beam for various beam current parts p are given in Table 2.
Figure 28. Photography of the set for measuring radial current distribution of EBW beam utilizing the method of Dr.Elmer. The tungsten sampling disc have 7 radial slits
Table 2. Relation between the values of the emittance and the part p of the beam current
p 0,63 0,78 0,86 0,99 εp 2ζx.ζx 3ζx.ζx 4ζx.ζx 9ζx.ζx
he emitt ance
p
and the stand ard devat ions
Figure 29. Plot for obtaining the coefficient C from beam current part p
The transformations of coordinate x and x in the drift space (that is free from external to the beam forces) are given in a matrix expression as:
1
On the base of the theorem for the dispersions of the sum of two random quantities and a zero value of the co-variance between x0 and x0 due to the canonic position of the emittance diagram in the cross-over image plane (called usually ―focus‖ or ―waist‖ of the beam) and using eq. (66) a system of three equations can be written:
(ζx1)2=(ζx0)2+(L0-1)2(ζx0)2, (67) measurements of the beam profile) are necessary.
The data evaluated from the beam profiles shown in Figure 19 and Figure 20 by that method are shown in Table 3. The signs are: p is the part of the beam current Im normalized by the total beam current I0 .The values ar and br are the ellipse axis values of the respective parts, including chosen part of the beam current. Index p defines the evaluated emittance and relative brightness.
Design of High Brightness Welding Electron Guns and Characterization… 41
Table 3. Evaluated data of the studied EBW gun with a bolt cathode
P=Im/Ib - 0.39 0.63 0.78 0.86 0.99
K - 1 2 3 4 9
ar mm 0.222 0.313 0.384 0.444 0.666
br mrad 10.92 15.4 18.9 21.84 32.76
p mm mrad 2.42 4.85 7.27 9.7 21.8
np m rad 1.17 2.35 3.52 4.7 10.56
(B/U)p 105A/m2rad2V 8.87 3.56 1.96 1.22 0.277
Another method for the calculation of emittance using slits and a deflected beam with a changing place of the beam ―focus‖ ("waist")were proposed in [18,22]. This method was applied for evaluation of emittance in x0x' and y0y' planes. For that aim the beam was crossing through two perpendicular slits and two measured signals of passing electrons at continuously changed focusing coil current was measured. Let see the signal use for calculation of one emittance x .
In the investigated cross-section is situated water-cooled input plate with a narrow slit.
The beam is deflected across that slit. From a previous investigation the relations between some values of the focusing coil current and the focusing length of the electron gun magnetic focusing lens f , knowing also the corresponding positions of beam ―waist‖(or so called
"focus") planes zbf1, zbf2 and … zbfi are known. Please, do not mix the focusing length f of the electron lens with the distance between central plane of focusing lens and crossover image plane (namely beam "waist", called usually also as beam ―focus‖ plane).
The base electron lens equation is used:
f 1 z z
1 z
z 1
fl bf fl co
. (70)
There zco is the cross-over place on the beam axis; zbf is the place of the beam ―focus‖
(image plane) and zfl is the central plane position of the magnetic focusing lens of the electron gun (see Figure 30).
Figure 30. Measuring the beam current distribution by changing the position of the focal plane
For the calculation of the standard deviations of the normal distributions of electrons at the beam ―focusing‖ planes (images of the cross-over) at various focusing lengths ζi0, …, ζn0
the coefficients of magnifications ki are calculated by :
i position of the emittance diagram, one can find ζx0i at measured ζxi.
In [24] was proposed a third method of emittance observation through adding a second thin focusing lens, that transforms the angular beam distribution in radial one. The studied beam cross-section before lens is crossing by a moving slit along x. The output signal, that is a transformation of x‘ to x, obtained by output slit in suitable position after the lens is given on y axis of an oscilloscope (on x is given signal, produced by x movement of movable slit.
The emittance diagram is observable directly on the oscilloscope screen.
In the all shortly discussed methods where a slit is applied for sampling a line integral of beam current distribution the parameters of: i) slit wide W, ii) modulator slit thickness H (in its narrower part, see Figure 24) and iii) angles between slit walls in out in input or output orifices of slit channel, as well as iv) the distance between two neighbor slits LS have to be optimized for the certain value of the emittance to be measured. The following criteria have to be fulfilled for a correct emittance evaluation.
Angular acceptance of the slit must be significantly bigger than the maximal beam divergence. Distance L have to be enough big. So:
in 10o ; out 10o . (74)
Design of High Brightness Welding Electron Guns and Characterization… 43