Pre-Christmas brainstorm on s.c. compensation for PS or PS booster

participants: MA, GA, UD, JPK, MM, YP, WS, FZ 


Masamitsu and Ulrich gave two presentations on tracking with space charge and
electron lenses. Jean-Pierre clarified that they only consider direct space-charge 
effects. PS booster parameers were reviewed. MAsamistu's simulation is only
2-D at the moment, Ulrich commented on the flat longitudinal bunch shape with second
harmonic rf system and possible ways of imlpementing this. The two codes are 
independent.  Masamitsu checked the lattice and the s.c. tune shifts.

For compensation he installed 1, 2, o4 4 e-lenses symmetrically around the ring.
He assumed a lens length of 2 m. The horizontal tune shift could not easily be
compensated, which seems to be related to the horiozntal integer tune of 4, which
is commensurate with the e-lenses. The lack of compensation was indeed shown
to depend on the bare tune as well as on the size of the effect.
The 4 lenses drive resonances corresponsing to the integer tune of 4, which
seems to be a pathological case.

Masamitsu showed that under certain conditions the e-lenses can greatly reduce the
tune spread. It was commented that his e-current of order 1 A was compatible
with the FNAL TEL current. The LEIR e-cooler was quoted with 2.5 A current.
The proton intensity considered corresponded to the LHC ultimate intensity without 
losses. 

Near-term goal could be to find a scheme whioch does not excite resonances, e.g.,
with proper choice for the number of lenses and integer tune. In Masamitsu's
simulations, synchrotron motion was not considered. Instead he modelled a 
coasting Gaussian beam. An laternative approach could be the compensation via
octupoles, on which Yannis commented later.

Ulrich discussed s.c. amnd e-lens extension of his code BBTRACK. Two options are
rigid Gaussian and soft Gaussian. The longtudinal density profile can be 
selected as constant, Gaussian, or read from a file.  
The e-lens is considered to be noiseless and round. 
The e-lens could be either pulsed, or one might contemplate a partial compensation
with a dc lens.
Ulrich exlpained how the bunch flattening h=2 RF system affects the distribution.
He asked whether it would make sense to include the t-dependent RF in the simulation.
Next goal is to implement noise sources.
PS booster mad-x file was just released by O. Berrig. 
Ulrich uses the mad-x fiel to get the transport matrices needed by his code.

Michel exlpained that the h=2 RF is switched on adiabatically duiuring a few ms,
whereas the revolution period is 1.7 microsecond, and injection lasts over 
10-15 turns, during which 40% of the beam is lost on the septum, not linked to
space charge. Also, with the new linac4, tjhe booster would be less subject 
to space charge. It could be that the PS should be our playground.
Walter commented that it is important to consider a realistic scenario, and
to assume the hardware we actually want to use, plus errors.
It was discussed whether the intensity of the e-gun can be modulated to match 
the profile of the protons. Frank thought yes, based on TEL experience. 
This question could be clarified with Vladimir. A related question would
be the pulsing frequency. 

Gianluigi commented that there is no space for e-lenses in the PS booster.
Actual length requirements for an optimized system need to be defined. 
Walter suggested concervign a new type of length adapted to our application.
The PS booster already contains numerous multipoles for resonance compensation.
The available space should be determined (Gianluigi?).

Jean-Pierre suggested that our strategy be to first demonstrate that the
compensation works in principle and then think of the implementation in a 
second step. Walter recommended to perform simulations for the most
probable conditions. A test in the PS could be a possibility.

Yannis reviewed the idea of space-charge compensation using octupoles.
The fields are expended in a power series. Different analytical expressions
for the space charge exists, from as early as 1972 (E. Keil), over
1993 (M. Martini), E. Metral and Ruggiero, etc., using elliptical
integrals, Bessel functions, or other expansions.
E. Metral and F. Ruggiero already studied the effect of octupoles on
Landau damping with sapce charge. Octupoles at the SNS are mainly intended
for Landau damping. The octupole strength required needs to be computed still.
Available PS octupoles are certainly strong enough (factor 20 margin).
Simulations for PS injection could be run with the codes ACCSIM and ORBIT,
both installed at CERN. 
Perhaps the compensation can also be tried in the PS booster, if octupoles
are available there.  MAchine experiment in the PS is another approach.
Also sextupoles may be put to good use. 
In the PS there are three types of octupoles: Landau damping octupoles,
extraction octupoles, and octupoles for the new extraction scheme.
Walter asked how resonances can be avoided. Jean-Pierre noticed that for 
beam-beam  octupole compensation did not work. 
Second order chromaticity must be confined if octupoles are used. 
A reasonable arrangement of octupoles should be found. 
Andrea Franchi has learnt the use of ORBIT.

More manpower may be needed to make progress on space-charge modeling
with ACCSIM and ORBIT. One possibility could be the Marie-Curie programme,
another possibility is that Masamitsu takes on the ORBIT code. 
These tools are appropriate and well understood. ORBIT is modular, and
exist in various versions from its authors. Jean-Pierre recommended 
considering resonance-free octupole schemes as had been studied for
LEP and LHC.

Jean-Pierre reviewed space-charge compensation schemes implemented at the 
ISR, which helped to raise the current from 4 A to 45 A (physics) / 50 A (MD).
Indirect space charge was the bread and butter at the ISR. 
There were three effects limiting the ISR current, including a RW instability.
A 1-MHz feedback was later expanded to 50 MHz without achieving the 
expected improvement. 
A characteristic feature was the online compensation of the space-charge detuning,
based on the longitudinal Schottky signal, which provided information on
dI/dx. Pole-fase windings were used to correct the tune shift and the next 4 orders
in its Taylor expansion with respect to the 1/2 aperture. There were 24 PFWs in total.
Zotter's curves were used for computing the correction needed, which was applied
for every 3 A of additional beam current. 
The reshaping of the betatron tune distribution was also guided by BTF measurements.
The transfer function provided the transverse distribution. A cyurved working line was
chosen for various reasons. 
The ISR established a sophisticated control with a single computer,
which led to a 100-fold increase of luminosity.

It was discussed whether the PS coherent instabilities could be suppressed by
dipole and quadrupole feedback systems. Fleming Pedersen and Elias Metral might
provide more information. 

Jean-Pierre proposed looking at the indirect space-charge force of a s.c.
beam pipe. What would be the effect on the coherent and incoherent tune shift.