According to the stochastic model the diffusion coefficient a in direction of retrograde motion should have no dependence upon the transverse field component or the normal field gradient (see Equation 5.2). This section briefly describes a short experiment conducted to test the existence of any such dependence.
5.4.1 Experimental details.
Using the equipment and software described in detail in Section 5.3.2 velocity distributions were measured for a range of coil settings (and hence transverse field strengths and normal field gradients). All experiments were conducted on a titanium cathode in a background pressure of 0.75xlO3 mBar of argon, at an arc current of 70A and with the normal field zero set at 19 mm.
Thirty runs were conducted (the first four of each group of five were used to condition the cathode). Each run again consisted of the timing of 2000 orbits of the arc spot. At every fifth run the coils were adjusted to the required field setting and data collected. At the thirtieth run the coils were reset to the currents used at run five. This allowed an estimate for the overall trend in the diffusion coefficient to be made at a constant field
(i.e. the trend of a with depth of erosion) and an approximate correction applied to data collected at different field settings.
The results were analysed by software as described in Section 5.3.3 and the best fit values for v and a obtained for each field setting. Table 5.5 shows the field settings used and the values for v and a calculated.
Table 5.5
Values of v and a obtained at different magnetic field settings Run number (mTesla nr1) b t (mTesla) V (m s_1) a (m2 s*1) 5 1270 11.69 20.5 2.82 10 1213 11.2 20.0 2.61 15 1161 10.33 19.42 2.25 20 1066 9.89 18.85 2.43 25 992 9.29 18.32 2.71 30 1270 11.69 23.0 2.05
5.4.2 Results and discussion.
Figure 5.25 shows the values obtained for a plotted against transverse field, the two points at 11.69 mTesla being the fifth and thirtieth runs. Examining this graph several points become apparent. Firstly it is possible that the diffusion coefficients obtained for runs 5 to 30 are the same within error (one result in three would be expected to lie outside one standard deviation from the mean). Secondly the a value obtained for run 30 is substantially lower than those for the previous 25 runs. This would seem to indicate that the possible trend (noted in Section 5.3.4.3) of decreasing a with depth of erosion due to some confining effect of the track is being exhibited here. Thirdly,
assuming that there is a trend apparent within runs 5 to 25, this would seem to show an initial decrease in a with decreasing transverse field up to run 15 (in opposition to the trend observed in Section 5.3.4.3). This followed by an increase in a with decreasing transverse field for runs 20 and 25. Finally the values for transverse field given are those measured for a flat cathode: some correction to these values (up to 10% in the case of run 30) must be expected.
Change in diffusion coefficient with transverse magnetic field 0.0035 j 0.003- 0.0025 - 0.002 c a 0.0015 o ® g 0.001
Is
0.0005 * 0 a ‘3 8 ^ - £ □ B “ K> t-J o - □ 5I? nRun 5 n Run 30 n Alpha ~ Error ** Error 10 10.5 11 11.5 12 12.5 13Transverse field component (mTesla)
13.5
Figure 5.25, Change in diffusion coefficient with magnetic field.
Considering these facts one possible explanation for the observed trend is as follows. For runs 5 to 15 the transverse field magnitude and normal field gradient are high. The spot is thus well confined and, as a track is eroded and the spot confined further, the amount of diffusion is reduced. At some point between runs 15 and 20 a field setting is reached where the spot is no longer so well confined that it must reside in the eroded track and can play upon the flat cathode surface. This would have two consequences; firstly the magnitude given in Figure 5.25 for transverse field at these points is likely to be a more accurate measure of the field there, i.e. whilst the spot is moving outside the track there is no artificial increase in the magnetic field to be considered. Secondly if the existence of the trench does have some confining effect upon the spot then this
confinement will be lost when the spot moves out of the trench. These two effects may combine to decrease the amount of confinement of the spot and so more diffusive behaviour is exhibited. At run 30 the spot is again confined to the trench by a stronger field (also now increased by the depth of the track) and the amount of diffusion reduced accordingly.
Considering the number of effects at work upon the spot during this experiment it is hard to draw a firm conclusion pertaining to the change in spot diffusion in the direction of driven motion with magnetic field or even whether there are any changes. There remain a number of experiments to be performed to separate the dependencies of spot diffusion upon spot confinement, spot confinement upon track depth and the erosion profiles produced by differing field profiles. This section is the subject of discussion in Chapter 6 where possible further work is suggested to test these dependencies.