the refinement of the curvature of the helix while the
longitudinal ∆z was selected such that the pitch-to-pitch
spacing was well resolved. In these cases, 50 transverse
cells (in each dimension) spanning the beampipe and 10
cells longitudinally (pitch-to-pitch) gave acceptable
results. Excitation waveforms were either simple ramp
functions of the form shown in Figure 2, or corresponded
Ez(t) sampled outside the helix.
Ez(t) sampled inside the helix.
Waveforms sampled every 12.5 mm
Waveforms sampled every 12.5 mm
to actually waveforms used as part of the experimental
2
2
1.5
1.5
tests as shown in the next section in Figure 4.
1
1
0.5
0.5
0
0
-0.5
-0.5
-1
-1
-1.5
-1.5
-2
-2
-2.5
-2.5
-3
-3
-3.5
-3.5
0
10
20
30
40
70
80
50
60
0
10
20
30
40
70
80
50
60
time (ns)
time (ns)
Figure 5a,b,c: the measurement points inside and outside
of the helix illustrate the unbalanced fields immediately
feed wire
outside of the helix.
At this point, it is envisioned that the ions would be
injected at a specific time to catch the accelerating portion
Figure 3: the feed wire attached to the helix at a point a
of the helical fringe field and/or the ion injector would
short distance into the supporting beam tube.
overlap the helix. From the time domain waveforms, it is
apparent that if ions are injected with an initial velocity
above (0.55%)c = 0.0055 × 3 108 m/s, and are timed to
reach the flat-top of the accelerating field at a spatial point
EXPERIMENTAL DATA
just inside the helix, then the ions will get from the z=z0
Early experimental data [3] confirming the validity of
points (at the helix boundary) to the z=z0+25mm point
the various models illustrates the benefits of full wave
(25mm inside the helix) in 15ns thus avoiding the
time domain simulations. These simulations include the
decelerating pulsed caused by the leading edge of the
source and feed effects, inductances near the beginning of
ramp waveform.
Note however that this ramp
the helix, transmission line effects, turn-to-turn coupling,
waveform's leading edge is much larger than what would
cross-turn coupling, and interactions with the enclosure.
be used in practice. It is also fortuitous that there is no
For comparison purposes, Figure 4 shows the comparison
decelerating field outside of the helix while the drive
between the simulation data and the results from the
waveform is building up. Thus particles outside the of
experiment for the input and output waveforms to the
helix can have injection energies corresponding to
helix.
velocities nominally less than (0.55%)c as long as they
Experimental data (helix #1)
Briggs, Waldron, Acc. HEDP workshop, Oct 2004
gain sufficient energy from spatial points 37.5mm
3D electromagnetic simulation
4
Output
3.5
Input
upstream of the helix (e.g. z=z0-37.5mm to z0) to achieve
3
3
2.5
a velocity of (0.55%)c by the time they reach the helix
2
2
1.5
1
1
boundary (see Figure 6). Also in this example, in order to
0.5
0
0
0.000E+ 1.000E- 2.000E- 3.000E- 4.000E- 5.000E- 6.000E- 7.000E- 8.000E- 9.000E- 1.000E-
-0.5
track the advancing accelerating wavefront once inside
00
07
07
07
07
07
07
07
07
07
06
-1
-1
-1.5
the helix, it is necessary to have a velocity of (1.2%)c at
-2
-2
-2.5
-3
the z=z0+25mm point or to have an earlier injection time
-3
Time [sec]
-3.5
0
100
200
300
400
700
800
900
1000
500
600
time (ns)
and accept the "slippage" along the advancing
Figure 4: comparison between simulation result and
accelerating wavefront.
experimental data from Briggs, Waldron [3] for the initial
prototype helix
helix windings
RESULTS
Initial work with the ramp waveform examined
matching the ion beam from an injector into the input of
helix windings
the helical structure. Field sensors at locations indicated
in Figure 5a show thirteen measurements points to
Figure 6: an expanded view of the input to the helix
illustrate the transition from outside of the helix to inside
shows the helix windings and the fringe region outside of
of the helix. The electric field plots shown in Figures 5b,c
the helix.
show the fields in the two groups of measurement points
as indicated. Note that there is one point of overlap
between the two plots.