Effect of off-axis beam through the buncher
Julian McKenzie
Updates:
19/05/2009
20/05/2009
1.
Removed mode 2 plots and added GPT tracking (sections 3 and 4)
Redid a load of sims for sections 3,4,5.
Introduction
Steering the beam through the injector beamline has proven to be tricky especially
with the influence of stray/Earth fields. Recent simulations [1] show that this effect is
especially important at our current gun voltage of 230 kV and therefore we are likely
to enter the RF cavities off-axis. For the buncher this effect could be particularly
important.
Current tracking simulations in ASTRA and GPT use a simple model of the buncher
cavity where the code takes the Ez field on axis and uses approximations to find Er
and Bφ. However, since these do not take into effect the cavity/beampipe geometry,
off-axis these fields are inaccurate. Only a 3D model of the fields would show an
effect.
2.
Buncher fields
The buncher cavity was previously modelled in CST Microwave Studio.
Fig2.1. The buncher cavity
Various modes can be calculated. In the following plots, the fields are all given at
1 Joule input energy [2]. So will be scaled down when doing tracking.
2.1
Mode 1 E-field
Fig 2.2
This is the main accelerating mode at the peak accelerating phase. You can see that
there is only a small transverse component but this increases with radius. Also note
that we operate this at zero-crossing where this field is at a minimum (but only when
the beam is at the centre of the cavity!).
2.2
Mode 1 H-field
Fig. 2.2
At zero-crossing the E-field is a minimum, therefore the H-field is a maximum. At the
bunching phase, it looks like this, looking down the beampipe.
3.
On-axis particle tracking with GPT
The E and H fields were exported from CST Microwave Studio with a 1mm grid in all
3-dimensions. To scale this down to the 1.3 MV/m peak fields as suggested by the
Astra simulations [3] for the 230 keV gun setup, we have to scale this field down by a
factor 0.03 since CST calculates the fields for 1 Joule of stored energy [2]. These
fields can be imported into GPT for tracking using elements not included in the
standard GPT release [4].
In the following simulations, the beam profile from [1] is used at the entrance to the
buncher. This is the beam profile for 10,000 macroparticles created through tracking
with GPT for the 230 keV injector setup not including stray fields into the calculation.
This is shown in Fig3.1
Fig 3.1: Density profile of beam at buncher entrance.
First a comparison was taken for the beam with tracking through 1D and 3D fields onaxis. In these simulations, the centre of the buncher cavity is at 1.3 m. The start of the
simulation is the beginning of the beampipe as shown in Fig 2.1. The buncher was set
to zero-crossing at the bunching phase. 1000 macroparticles were used for the
tracking
Fig 3.2 shows the 1D field case and Fig 3.3 shows the 3D field case. These plots show
the trajectories of the macroparticles in the y-z plane. As can be seen the trajectories
look largely similar. This shows that the expansion for fields close to the axis is
accurate.
Fig.3.2: 1D buncher fieldmap
Fig 3.3: 3D buncher fieldmaps
However, investigating this same situation with a larger beam with a halo, as seen in
Fig 3.4 shows different results. The tracking of the core beam remains the same with
both 1D (Fig 3.5) and 3D (Fig 3.6) maps but in the 3D case, stray particles off-centre
get focussed into the core of the beam. This shows how the approximation for Ez for
the 1D field case is not accurate off-axis.
Fig 3.4: Density plot of a larger beam with a small amount of halo particles
Fig.3.5: 1D buncher fieldmap with large beam
Fig 3.6: 3D buncher fieldmaps with large beam
4.
Off-axis particle tracking with GPT
The beam from Fig 3.4 was then started with +5 and +10 mm in the y-direction. The
three plots below show density profiles and the beam trajectories.
Fig 4.0: Beam y + 0 mm.
Fig 4.2: Beam y + 5 mm.
Fig 4.3: Beam y + 10 mm.
You can see that although the beam size stays the same, the beam is kicked a little
further off-axis. It should also be noted that the buncher aperture is the smallest in the
whole injector beamline. With the +10mm case above we are on the limit of this and
may already be losing particles to the beampipe, especially just after exiting the
buncher cavity
5.
Kick as a function of distance off-centre
These simulations were repeated for a range of different initial offsets and then the
angle of the kick calculated using the change in average y position of the
macroparticles. This is shown in Fig 5.1 and varies linearly as a function of initial
offset. This only accounts beams entering the buncher on-angle. The final 10 mm
point for 3D fieldmaps does not follow the trend because at this point some of the
beam is outside the buncher aperture of 13 mm where the 3D fieldmap stops, however
the 1D fieldmap has no boundary conditions.
Fig 5.1: Vertical kick versus initial beam offset. Red dots are using 3D fieldmaps,
blue using 1D fieldmaps
initial offset [mm]
0
1
2
3
4
5
6
7
8
9
10
<y> [mm]
0.01107
1.274
2.538
3.802
5.067
6.329
7.594
8.857
10.12
11.34
12.36
<y> - offset [mm]
0.01107
0.274
0.538
0.802
1.067
1.329
1.594
1.857
2.12
2.34
2.36
angle [mrad]
0.0369
0.913333
1.793331
2.673327
3.556652
4.429971
5.313283
6.189921
7.066549
7.799842
7.866504
angle [degrees]
0.002114
0.05233
0.10275
0.15317
0.203781
0.253819
0.304429
0.354656
0.404883
0.446898
0.450718
References
[1]
[3]
[2]
[4]
<\\apsv4\astec\Projects\4gls\ERLP\Machine operations\Alice injector
modelling with stray fields v3.doc>
Monika Balk, CST, private communication
<\\apsv4\astec\Projects\4gls\ERLP\Machine operations\Baselines Inj 230kV,
4.8MeV v.01.pdf>
Bas van der Geer, Pulsar Physics, private communication