Study of Long-Range Collisions and Wire-Compensation for the

Tevatron

Frank Zimmermann

February 21 – March 8

Thanks to: Bela Erdelyi, Paul Lebrun, Tanaji Sen, Vladimir Shiltsev, XiaoLong Zhang

motivationwire compensation is under study for the LHC with3 prototype wire-devices in the SPS

is there a potential for wire-based compensation of long-range collisions at the Tevatron?

situation is more difficult: helix (both transversedimensions), many betatron phases, differences between bunches and between injection & collision,dispersion, coupling, etc.

is it helpful to compensation a few “most harmful”long-range collisions? can I confirm the efficiencyof wire correctors found at injection?

which parameter can guide the compensation?

I looked at • bunch A1 at injection “cog0” (A1 stays longest in the

machine and was studied by B. Erdelyi and T. Sen) • bunches A6, A1 and A12 in collision

injection parameters

collision parameters

Phase-Space Positions of the Long-Range Collisions

Image of all LRBB collisions mapped into normalized phase space.

x-px y-py

x-px y-py

injection, A1

collision, A6

injection, A1

collision, A6

Normalized distance versus index of LR collision.

Ax Ay

AxAy

injection, A1

collision, A6

Distance Ay vs Ax (left) and total distance Atot(right) vs. index of LR collision.

Ax

Ax

Ay

Ay

Atot

Atot

LR encounters below 7 for bunch A1 at injection:

LR encounters below 7 for bunch A6 in collision:

6

3

Tracking is performed usingan extended version of WSDIFF

described at LHC99.

15 trajectories with random start amplitudes between 0 and 10 over 500 turns.

phase spacex-px y-py

coordinates vs time

injection, A1

xy

Tune Footprints

tune footprint for start amplitudes up to 6in each plane

all LR encounters without the 6 closest

injection, A1

not much difference…

injection, A1

comparison of footprints from WSDIFF with BBSIM

tune footprint for start amplitudes up to 6in each plane

all LR encounters without the 3 closest

collision, A6, w/o head-on

a large difference!

collision, A6, A12, A1

w/o head-on

Bela’s solution for wire compensation at injection (4 wires,which optimized dynamic aperture and/or minimized normof the nonlinear map)

tune footprint for start amplitudes up to 6in each plane

LR encounters only with 4 wires

injection, A1

footprint ‘rotates’, but keeps similar extent

Diffusion

launch group of particles at the same amplitude with a random phase and

compute increase of the average action variance per turn

(scheme of John Irwin for the SSC)

injection, A1

X Y

X Y

all LR encounters

without the 6 closest

dynamic aperture ~6 dynamic aperture ~5

injection, A1with 4 wires

~0.5improvement in Y

(note different horizontal scale on this plot)

dynamic aperture ~5.6dynamic aperture ~5.6

collision, A6

all LR encounters

without the 3 closest

X Y

X Y

dynamic aperture ~8

dynamic aperture ~8

~8.5 ~8.5

collision, A6

all LR encounters

with only the 3 closest!

X Y

X Y

dynamic aperture ~9.0 dynamic aperture ~9.5

dynamic aperture ~8 dynamic aperture ~8

collision

all LR encounters, A1

all LR encounters, A12

X Y

X Y

dynamic aperture ~6 dynamic aperture ~6

dynamic aperture ~5dynamic aperture ~5

Analytical estimates

tune shift, chromaticity, coupling,chromatic coupling, diffusion

tune shift & coupling

horizontal & vertical tune shift

A6

A1

A12build upover allLRencounters

injection

collision

collision

collision A1

real & imaginary coupling

A6

A1

A12build upover allLRencounters

injection

collision

collision

collision A1

chromaticity &chromatic coupling

horizontal & vertical chromaticity

A6

A1

A12

injection

collision

collision

collision

build upover allLRencounters

A1

real & imaginary chromatic coupling

A6

A1

A12build upover allLRencounterscollision

collision

collisioninjection A1

Total tune shifts, chromaticities, coupling driving terms, and chromatic couplings induced by long-range collisions for various pbar bunches in collision:

and for A1 at injection:

diffusion coefficient in 4D

no analytical solution yet for this double integral…

Future Plans

• extend simulations to 6D andcompute diffusion at 1

(chromaticity & chromatic coupling most likely important)• continue analytical calculations• study effect of unequal beta on

compensation• other suggestions welcome!