(1)
The current of the ion beam extracted from the Laser Ion Source is typically 60 mA of a mixture of high charge-states. Beams of such high current undergo a large self space-charge effect, which can lead to a rapid expansion of the beam (space-charge blow-up). Taylor et al. [1] have shown space-charge cross-over in non-uniform beams, causing highly-aberrated beams.
A zero emittance beam consisting of 60 mA (of
uniform current density) starting with an initial diameter of
3 cm, will grow to a diameter of 20 cm after a drift
space of 1 m (at 7 keV/u). Equation (1) gives the expansion
of a single charge-state, zero emittance uniform beam, where r
is the beam radius, ro is the initial beam radius,
z
is the charge-state, I the beam current, mi
the ion mass, vb the beam velocity and t
the time.
(1)
High velocity ions in a vacuum can cause ionisation
of the rest-gas molecules, resulting in separate positive and
negative charges. The electrons can be used to compensate for
the space-charge of the ion beam (see [2,3]). There are two important
time constants that must be considered to allow for the compensation
of the beam. Firstly enough residual molecules must be ionised
for the effect to take place. This can be estimated from the cross-section
for beam induced rest-gas ionisation, such that
(2)
where n is the particle density of the gas,
s
is the cross-section and v is the velocity. The sum must
be performed over each gas type in the vacuum. Taking reasonable
values for the cross sections for N2 ionisation by
protons, this indicates that not enough molecules can be ionised
to provide full space-charge compensation, but some degree could
be possible.
The second effect is for the time required rest-gas
ion to leave the potential well of the ion beam. Considering the
field in a uniform beam, the transit time for a charged ion of
mass number A to leave a beam of current I and radius
r0, is given by
(3)
where vb is the beam velocity and
mp the atomic mass unit. This can be written
more usefully as:
(4)
Therefore one can estimate that for a 60 mA
beam of 5 cm diameter the transit time is of the order of
0.54 ms
for N2+, but reduces to 0.1 ms
for H1+. It is therefore theoretically possible
to produce some degree of space-charge compensation within the
5 ms
beam from the LIS.
Although full compensation of the beam appears to
be unlikely, it may be possible for the compensation degree of
the beam to vary greatly along its longitudinal position. When
trapped within the potential well of the ion beam, electrons will
undergo oscillations in the transverse direction. Near a beam
focus a longitudinal electric field will also exist, the strength
of which can be estimated by the solution of the following integral,
(5)
Figure
1. Full line - longitudinal electric field
strength for a 60 mA ion beam about a beam focus of 1.5 cm
radius and 100 mrad half divergence. Dotted curve - beam radius.
This gives the longitudinal field component shown
in Figure 1, where a beam with the radius given ro=(rf2+a2l2)1/2
(c.f. equation (1)) has been used where rf
is the beam waist radius and a is the divergence angle.
From this figure one can estimate that an electron can travel
a distance of 10 cm to the focus in less than 0.5 µs,
but will oscillate around this position. If a large number of
electrons are available, they will all oscillate around the focal
position and lead to a reduction of the space-charge in this region.
This effect may also lead to an enhancement of the space-charge
in regions away from the focus where the residual-gas ion are
left.
To assess the effect of residual-gas space-charge
compensation, the plasma from the Laser Ion Source was extracted
at 60 kV using an accel-decel system (with the puller electrode
at -10kV [4]) with apertures of 20 mm and a distance between
the first two electrodes of 20 mm. In previous experiments
an average current of 38 mA (in the time interval from 3 - 8 µs)
had been measured with a Faraday cup 120 mm after extraction.
The first solenoid (see Figure 2) was used to provide focusing
and therefore a measurable spot size at the phosphor screen (P47)
detector. A pepper-pot, (which was isolated and held at 240 V
and capacitively backed) was used to reduce the beam intensity
and avoid damaging the phosphor screen.
Figure 2.
Schematic of the layout of the LIS single solenoid LEBT used for
the residual gas compensation experiments.
To increase the rest-gas concentration, N2 was bled in through a valve. As the gas bleed, pumping group and pressure gauges are all close, a residual gas analyser (located on the opposite side of the main expansion tank from the pumping group) was used to measure the background gas pressure.
The light intensity from the phosphor screen was captured with a gatable CCD camera. The camera was gated over the known high charge state group at 3-8 ms after the laser pulse. From the images the FWHM beam size and the beam intensity at the spot centre were recorded from an average of three shots.
The solenoid was used at two different fields (1700 A
and 1900 A solenoid currents). Due to the problems producing
reliable simulation - experiment, it is not known where the focus
lies for these solenoid settings. The results are shown in Figure 3.
Figure 3.
a) Ion beam width measured after the solenoid for different gas
pressures, for two different solenoid field settings. b) Peak
intensity of the spot under the same conditions.
The ion beam diameter can clearly be seen to change
as a function of the residual gas pressure. Conventional theory
would suggest that the ion beam should decrease in size with higher
compensation, whereas the data shows an increase in beam size
with increasing pressure. This could be primarily due to two possible
reasons:
The two cases have been investigated using simple simulations of the beam through a solenoid, with different beam currents. Only one charge-state may be considered.
For the first case, compensation and decompensation degrees of around 20% only lead to a 5% variation of beam size.
For the second case, a uniform reduction in the beam
current was assumed and the resulting beam widths at the detection
plane is shown in Figure 4. A radially symmetric beam was used
with linear space-charge and the focal length of the solenoid
was estimated from the formula f~4p2/q2B2L
where p is the ion momentum, q is the ion charge,
B is the average magnetic field on axis and L is
the solenoid length.
Figure 4.
Simulated beam width under different space-charge conditions for
two different solenoid filed settings.
Variation of the beam width up to 50% can be seen,
which is comparable with the experimental case. However, for both
solenoid conditions to give increasing beam size with background
pressure, the compensation degree must be of the order of 50%
or more throughout the beam, which appears to be unlikely. The
crossover in beam size of the two distributions for 1700 A
and 1900 A in Figure 3, occurs in Figure 4 at a higher beam
current than was measured experimentally.
Initial measurements have been performed of the effect of rest-gas pressure on the dimension of the Laser Ion Source beam. The results show that there may be an effect due to partial space-charge compensation. Simple models of the beam expansion and focusing give qualitative suggestions that the compensation must be along a high longitudinal proportion of the beam, and is not just due to effects after the solenoid and before the detector.
Further work should concentrate on modelling non-uniform
charge-density beams and testing further cases (in particular
for simple drift space) experimentally.