To assess the critical magnetic field lines escaping radially to the region where high density conics are normally formed, a radial-facing RFEA (shown as A in figure5.1) was used to map the density in the region downstream of the magnetic nozzle. The RFEA was swept through axial positions fromz= 0 cm toz= 10cm and radial positions fromr = 0 cm tor = 15cm
in 1 cm increments. The resulting array combines over 150 measurements, forming a 2-D map of the total ion current measured by the RFEA collecting electrode. The measurements were repeated for values ofzextfrom 0 cm to 5 cm. The collecting orifice of the RFEA was aligned
such that it was kept perpendicular to the measurement plane (i.e. facing out of the page in figure 5.2) which stopped the orifice from directly facing a chamber wall or the extension tube. Figure 5.2shows the maps of total ion current measured for zext= 0,2,4 cm and the
no extension case (herein referred to as the “standard” case to maintain consistency with the nomenclature used in the previous chapter). For the zext = 0 cm case, the plasma density
outside the extension tube (r= 8 to15cm) between z= 1−3cm was so low that the RFEA
could not accurately measure anIC(VD) curve.
When the extension tube is contiguous with the source (zext = 0 cm, figure 5.2 (a)) the
total ion current can be seen to decrease both axially and radially with increasingz. As zext
increases (figure5.2 (a)-(c)), a number of changes occur. Firstly, the conics can be seen to form as hot electrons are permitted to escape radially through the geometric window. Secondly, the density profile can be seen to retreat upstream into the source as the distance between the extension and source tubes increases. As the electrons are now permitted to reach the region of the high density conics and ionise there, their residence time in the source decreases yielding less ionisation upstream and the topography of the density throughout the system approaches that of the standard case. In cases where the extension tube is included (figure5.2 (a)-(c)), the maximum total ion current in the mapped region is measured on axis, however the density of the conics is shown to increase with increasingzext. In the standard case (figure 5.2 (d)),
the maximum total ion current is measured in the conics and this configuration reflects the case in whichzext→ ∞. This shows that the electron transport to the conics region begins to dominate the behaviour in the mapped region as the extension tube is situated at increasing values ofzext. The reduction in total ion current on axis is in agreement with the axial density
measurements presented in the previous chapter (figure4.3), in which the density profile in the standard case was seen to decrease further upstream than when the extension tube was placed atzext= 0 cm. Here, the total ion current maps show the downstream density profile
transitioning between those shown in figure 4.3 as the geometric window increases and the conics reform.
While the maps presented in figure 5.2 illustrate the emergence of the conics and the retreat of the density profile into the source tube, they do not clearly indicate the shape of the conics density relative to the standard case. Figure 5.3 shows the total ion current measurements along an axial slice atr = 9cm for values ofzext= 0−5cm and the standard
case. The standard case data (filled triangles) shows an initial increase in total ion current fromz= 1 cm toz= 3 cm before achieving its maximum and decaying with a convex profile
to z = 10 cm. These characteristics set the benchmark for determining how similar to the
standard case the other cases may be.
Whenzext= 0 cm and the extension tube is contiguous with the source tube (unfilled tri-
angles), no electrons are permitted to escape to the region where high density conics normally form and the figure shows that the total ion current tends to zero for z → 0 cm, indicating
why a reliable RFEA measurement was not attainable for z = 1−3 cm. The ion current
can be seen to increase downstream as it gets closer to the end of the extension tube at
z = 18.5 cm, where plasma is released and is able to diffuse to the locations shown in figure
5.3 . Whenzext= 1 cm (diamonds), the total ion current has increased but does not reflect
any of the characteristics of the standard case. This is because the electrons following the first escaping radial magnetic field line from the source collide with the front face of the extension tube due to its thickness. However, as there is still a 1 cm window available for the plasma to escape through radially via cross-field diffusion, there is a small increase in the plasma density outside the extension tube resulting in the flat profile shown in figure 5.3. Whenzext further
increases to 2 cm (crosses), the density can be seen to increase dramatically, particularly at locations close to z = 0 cm, showing the effect of releasing the electron populations trans-
ported along the first magnetic field lines escaping through the geometric window. While the maximum total ion current of the zext = 2 cm case is comparable to that of the extension
case, the profile shows different behaviour. The data shows that the peak occurs much closer to z= 0cm than the standard case and the profile decays with a concave shape. These traits
are shared with thezext= 3cm case (squares), however the peak moves downstream by 1 cm
with the corresponding 1 cm increase in the geometric window. This behaviour changes when
zext increases to 4 cm (circles) and 5 cm (plus signs). Between these two cases, there is very
little change in the total ion current axial profile at r = 9 cm. While these profiles do not
exactly correspond to the standard case, they have a similar peak value and decay with a convex profile. Given the similarity of the zext = 4,5 cm profiles to the standard case and
that there is very little change between these cases, these measurements suggest that the most critical electron populations for formation of the conics have been released. This transition is deemed to have occurred when zextincreased from 3 cm to 4 cm and, as such, the critical
size of the geometric window is 4 cm. For windows smaller than this size, e.g. zext = 3 cm,
some critical electrons for conics formation must still be incident on the sheath surrounding the extension tube and do not reach the region where high density conics form. This explains why the density profile atr = 9 cm is concave, or depleted when compared to the standard
0 2 4 6 8 10 z-axis (cm) -15 -10 -5 0 5 10 15 r-axis (cm) z ext=0cm 0 2 4 6 8 10 z-axis (cm) -15 -10 -5 0 5 10 15 r-axis (cm) z ext=2cm 0 2 4 6 8 10 z-axis (cm) -15 -10 -5 0 5 10 15 r-axis (cm) z ext=4cm 0 2 4 6 8 10 z-axis (cm) -15 -10 -5 0 5 10 15 r-axis (cm) No Extension 0 0.2 0.4 0.6 0.8 1 1.2 1.4
Total ion current (arb. units)
(c) (d)
(b) (a)
Figure 5.2: 2-D maps of the total ion current collected using the radial-facing RFEA for
zext= 0,2,4cm and standard cases. Data was not available forzext≤3cm in thezext= 0cm
case outside the extension tube as the local ion density was too low and the RFEA is unable to measure reliableIC(VD)data. The lines illustrated in the zext= 4 cm case are FL1, the first
radial magnetic field line escaping from the source (solid black line), and FL2, the magnetic field line that just passes the outer corner of the extension tube (dashed black line).
0 2 4 6 8 10 z (cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Total ion current (arb. units)
r=9 cm Standard 5 4 2 1 0 3
Figure 5.3: Profiles of the total ion current taken along an axial slice atr= 9 cm (i.e. in the
conics region) for cases ofzext= 0cm (downward pointing triangles),zext= 1cm (diamonds),
zext = 2 cm (crosses), zext = 3 cm (squares), zext = 4 cm (circles), zext = 5 cm (plus signs)
5.3
Effect on the axial ion beam
Given that electron transport along magnetic field lines escaping the source to ionise in the conics is linked to axial ion transport, as shown in the previous chapter, it is interesting to determine if a transition in the beam characteristics also occurs by releasing the electron populations identified in the previous section. To determine this, a source-facing RFEA is used to measure the axial ion beam behaviour in the downstream region for increasing values of zext. Figure5.4 shows the beam velocities,vb, for values ofzext from 0 to 7 cm, calculated
using equation 2.12 from measurements taken using the source-facing RFEA positioned on axis at z= 7 cm. The axial region of ion acceleration is expected to transition between those
in the standard and zext= 0cm shown in chapter4 and therefore negligible ion acceleration
is expected atz= 7 cm for allzext. The figure also shows the beam velocity for the standard
case (black line) with the error bar of ±0.39 km/s (dashed lines) as was shown in chapters3 and 4. 0 1 2 3 4 5 6 7 z ext (cm) 0 2 4 6 8 10 v b (km/s) z=7 cm
Figure 5.4: Calculated values of the beam velocity atz= 7 cm found using the source-facing
RFEA measurements. The measured vb in the standard case is indicated by the solid black
line at ∼8.75 km/s with an error bar of±0.39 km/s given by the dashed lines.
When zext ≤ 3 cm, i.e. values for which the conics were shown to have not yet fully
formed in figures5.2and5.3, figure5.4shows that the beam velocity is relatively constant at the value of the zext= 0 cm case. When zext≥4 cm and the major transition in the conics
formation discussed earlier has occurred, the beam velocity goes through a step change to the value found in the standard case. As such, figure 5.4 demonstrates a transition in the
beam characteristics at the same critical size of the geometric window as that found earlier in relation to electron transport to the conics. As the ion beam is accelerated by potential structures upstream in all cases, the transition in beam velocity here must be reflected in the magnitude of the potential drop in the double layer-like potential structure. Therefore, by releasing the hot radial electrons through a geometric window 4−5 cm from the interface of the source tube and diffusion chamber, the axial plasma potential characteristics of the standard case have been retrieved.
The source-facing RFEA data used to calculate the beam velocities in figure5.4 can also be used to calculate the beam density,nb using the Gaussian-flux method. Figure 5.5shows
the calculated beam densities forzext= 0−7 cm atz= 7 cm. Also shown is the value of nb
for the standard case (black line). The data shows that the beam density on axis atz= 7 cm
decreases sharply by a factor of∼2−2.5 when zext is increased from 0 to 2 cm. This sharp
decrease innb aligns closely with the values of zext for which the beam velocities in figure5.4
have not yet undergone the step change to the velocity of the standard case. From the density maps in figure5.2, this coincides with the axial density profile retreating upstream into the source region before the conics are fully formed. Forzext= 3−7 cm, the figure demonstrates
a density gradient which is much less severe, reducing by a factor of∼2again until reach the
beam density of the standard case.
0 1 2 3 4 5 6 7 zext (cm) 0 1 2 3 4 5 n b (cm -3 ) 109 z=7 cm
Figure 5.5: Measurements of the beam density at z = 7 cm using the source-facing RFEA
and the Gaussian-flux method. nb for the standard case is indicated by the solid black line at
∼8.45×108 cm−3 with an error bar of ±10% given by the dashed lines.
standard case with increasingzext, the trend innb is much less striking than that observed in vb in figure5.4. While the beam velocity is just a function of the upstream and downstream
plasma potential, the beam density is dependent on many more parameters. These include the location and magnitude of the maximum upstream density, the location of the potential structure which accelerates the ion beam and the mean free path for ion-neutral collisions. For example, as zext increases, the results in figure 5.2 showed that the density contours
retreat upstream, an effect which would be reflected in the axial potential profile via the Boltzmann relation. This means that the beam would be accelerated further upstream and would therefore undergo more collisions with background neutral before being detected at
z = 7 cm. As such, it is difficult to assess the source behaviour and the effect of conics
formation from the measured beam densities in the same way that was possible with the measured vb.