,
(Eq.1)
An electron-positron Linear Collider (LC) in the 500 GeV – 1 TeV energy range has the potential to deliver interesting physics complimentary to current hadron colliders and is now widely viewed as being the highest priority machine to construct post-LHC (e.g. see UK statement of interest).
There are currently several designs, all at an advanced stage, in existence
for such a machine; TESLA,
NLC and
JLC are all designed to operate within this
energy range whilst the CERN design,
CLIC, uses an elaborate 2-beam technology
and is envisioned to extend into the several-TeV range.
In addition to high energies, the physics potential of such machines is enhanced
by the intended high luminosities O(1034 cm-2 s-1).
To maintain such high luminosities the electron beams need to be kept well
aligned, and with vertical beam sizes in all designs only in the order of a few
nm this places very tight tolerances on all accelerator components. It will be
essential that any of the LC designs incorporate automatic feedback systems to
maintain luminosity.
There are several distinct and subtle differences between the different design proposals, for detailed information the conceptual and technical design reports should be consulted. What are important to this study are the specifications relating to the bunch structures at the interaction point of the collider. Relevant data is presented in the table below, contrasting the different technologies of TESLA, CLIC and NLC.
|
Beam Parameter |
Machine |
||
|
TESLA |
NLC-H |
CLIC |
|
|
Particles/Bunch (x 1010) |
2.0 |
0.75 |
4.0 |
|
Bunches/Train |
2820 |
190 |
154 |
|
Bunch Separation (ns) |
337 |
1.4 |
0.7 |
|
sx/sy (nm) |
553/5 |
245/2.7 |
202/2.5 |
|
sz (mm) |
300 |
110 |
30 |
|
fr (Hz) |
5 |
120 |
200 |
|
Transverse Emittances gex,y (x 10-8 rad.m-1) |
1000/3.0 |
360/3.5 |
200/2 |
|
Beta Functions bx,y (mm) |
15/0.4 |
8/0.1 |
10/0.15 |
IP Beam Parameters for the different LC designs.
One of the main limiting factors in the performance of a LC is ground motion and vibration. This is caused by natural earth movement as a result of seismic activity or, for example, ocean waves and additionally by man-made disturbances; whether they are cultural above-ground sources or noise introduced by components of the machine itself. Such ground motion has the potential of degrading the luminosity performance of a LC by causing misalignments in the magnetic components, which then steer the beams away from their design orbits. There has been a considerable amount of study done on this subject (For example see the SLAC Ground Motion web pages). Figure 1, for example, shows some results from a SLAC study in the SLC tunnel near the SLD. Figure 2 shows the results of TESLA simulations on the effect of ground motion on the measured luminosity.
The left plot on
figure 1 shows how two points separated by 30m drift out of alignment over
time due to natural ground motion only. It can be seen that offsets due to
natural sources are relevant only really on timescales of greater than a second,
even where nanometre-scale colliding beam spot sizes are concerned. Feedback
systems like those that have been in use for some time at SLC can be used for
these timescales. For motion and subsequent misalignment on shorter timescales
than this, new feedback mechanisms need to be developed. Although natural ground
motion doesn’t seem to be an issue here (at this particular site- different
sites have different noise profiles), looking at the right plot in
figure 1 shows
the situation where cultural and machine noise is ‘added in’. With ground
vibrations at frequencies above 1 Hz, at night with little human activity and
SLD off, the amplitude of the vibrations is at the nanometre level. At times
where there is more cultural noise, and with the machine electronics on, the
noise amplitude grows by at least an order of magnitude to levels where
luminosity is going to be seriously impaired as the nanometre-scale beam spot
sizes wander off their collision axis. All components are being designed so as
to minimise vibration, although the tolerances on some components (specifically
the final focus quadropole magnets) are very tight. It is therefore extremely
desirable to have in place an automatic feedback system that is capable of
removing misalignments and keeping the beams in collision at the nanometer level
and at frequencies above 1 Hz. To do this, one can imagine constructing a
feedback mechanism that either adjusts the position of the mechanical structures
housing the magnets, or a different kind of system that actually re-steers the
beam, or indeed both. Studies are being carried out into the validity of an
‘optical anchor’ and also for other inertial stabilisation techniques to achieve
the first kind of solution
elsewhere. What is investigated here is the second
possibility of keeping the beams in collision by continuous steering of one or
both of the beams through the use of a kicker magnet close to the beam
interaction point.
Assuming a head on collision the design luminosity is given by:
,
(Eq.1)
where N is the number of particles per bunch;
sx,y are the horizontal
and vertical RMS beam sizes at the interaction point (IP) respectively;
is the pulse repetition rate of the collider and nb
is the number of bunches per train. The luminosity is further enhanced by a
factor HD . This is the so-called pinch effect and arises as a result
of the electromagnetic self-focusing of the electron/positron bunches. As an
ultra-relativistic particle in either the colliding electron or positron bunch
passes through the EM field of the opposite charged bunch, it experiences a
force due to both the electric and magnetic fields in the direction of the
centre of the bunch it is passing through. The forces due to the electric and
magnetic fields in the particles own bunch cancel each other out (to within 1/g2).
The pinch effect is defined with respect to a variable known as the disruption parameter:
,
(Eq.2)
where re is the classical electron radius and sz is the RMS longitudinal bunch size. The pinch effect is only analytically calculable for small disruption values- not applicable for future linear colliders that have large disruption parameters giving rise to substantial luminosity enhancement. In this case a parameterisation of HD from Monte-Carlo simulations is used:
. (Eq.3)
For negligible disruption the luminosity falls off according to the equation:
,
(Eq.4)
where Dx,y is the transverse beam offset in the x- and y-directions. As the ratio of horizontal (x) to vertical (y) beam spot sizes is of the order 100:1 for all LC designs, we are concerned with just the vertical offsets. According to the above formula, luminosity falls off exponentially with the beam offset. As can be seen in figure 3b, this is not what the simulations show. This is due to the presence of a large disruption parameter focusing the beams into one another even with considerable offsets.
In addition to luminosity drop-off, another more favourable consequence of offset beams is that as the offset bunches pass, each receives an electromagnetic kick from the other. The size of this kick is dependent on the size of the offset and is quite large (order of micro radians). This provides a useful signal on which to base the design of the feedback system. For small vertical offsets and a small disruption parameter the vertical kick experienced by the offset bunches is given by:
.
(Eq.5)
The actual profile of the beam kick as a function of offset in reality needs to be simulated as the disruption parameter is not small and things are further complicated owing to the fact that the beam size does not remain constant during the interaction due to the pinch effect. The calculated kick profile can be seen in figure 3a. It can be seen that the curve is highly non-linear, although for small offsets the above linear relation does approximately hold true.
From the perspective of a feedback system which needs to operate within one bunch train, the important parameters to look at (see table) are the number and spacing of bunches within the train. Here TESLA is the easiest environment for such a system with 2820 bunches to feedback on, and with 337 ns between bunches it is possible to design a digital system to feedback on every bunch. Such a system has been successfully tested at TTF. The situation with NLC and CLIC is considerably complicated by the fact that the trains only contain 150-200 bunches with bunch separations of the order of nanoseconds. The operation time of the TESLA digital solution is in excess of 200 of nanoseconds, which is obviously of little use for either NLC or CLIC. For these cases a faster analogue approach is required.
Despite the design differences, the planned method of correcting luminosity loss through vertical beam offset at the IP is similar for all.
The final focusing quadropoles (Q1) experience random movement due to ground motion on timescales comparable to the pulse repetition frequency which causes a vertical offset between the beams at the IP of order several sy. Hence, to first order, the first bunch trains arrive with all bunches at a constant offset; then Q1 moves around during the time between pulses and the next bunch train arrives at a new random offset. The feedback system then has to operate within each train as fast as possible to keep the bunches in collision and maintain luminosity.
The components of the fast feedback system at the IP are:
(a) A stripline Beam Position Monitor (BPM) to measure the outgoing bunches after collision i.e. the beam-beam kick which gives the sensitivity to small position offsets at the IP (as described above).
(b) A fast electronic processor to take the raw signals from the strips of the BPM and turn them into a signal for input into the feedback algorithm. This signal is proportional to the beam position in the BPM.
(c) The electronic feedback algorithm takes this signal and provides the correct signal to the correction kickers to reduce the signal from the BPM processor to zero, and hence maintain alignment of the beams.
(d) Stripline kickers take an amplified signal from (c) to charge themselves and impart an EM field on the incoming bunches to deflect them into alignment as per the instructions from the feedback electronics.
(e) External inputs to the system required are the bunch charge information needed to normalise the BPM signal, and user inputs to adjust the parameters of the feedback algorithm to the current operating conditions.
To realise a fast feedback system as outlined above, the designs of TESLA and that of NLC/JLC and CLIC are treated separately.
Here, a system based on a digital control system has already been designed and a prototype tested at TTF- the TESLA Test Facility. Ongoing work now is focussing on creating realistic simulations of how the system operates under different conditions using models of the whole accelerator. Specifically, looking at the "Banana" effect where the bunch shapes get systematically distorted due to short range wakefields in the superconducting RF cavities. It has found that this effect causes large losses in luminosity for small, immeasurable emittance growths and also affects the operation of the feedback system by altering the beam-beam dynamics.
For a review of current simulation progress and results see here.
These designs pose the most difficult constraints on a fast feedback system, where it must operate on the few nano-second level to minimise beam offset within the few hundred nano-second duration of the train. Here research is ongoing to test different simulations of how different proposed systems would operate in the interaction region of the collider itself. Also, hardware testing of the key components of the system are being tested, both on the bench and at an existing linear collider test accelerator facility- NLCTA.
See here for a review of current simulation work.
See here for progress with the hardware testing.