Tune spread control with Tevatron Electron Lens

Aleksandr Romanov

Vladimir Shiltsev

Alexander Valishev

Gennady Kuznetsov

Giulio Stancari

Some theoryBeam-beam effects, space charge and nonlinear

elements causes betatron tunes of particles in a circulating beam to be different. All variety of this tunes forms a tune-spread (footprint).

To avoid loss of the particle due to chaotic drift, its tunes should be located away from harmful resonances.

Beams intensities are often limited by maximal size of footprint that can be fitted between resonances.

• Several things pushe particles to harmful resonances:– Tune spread in one bunch could be too big to fit between resonances– Circulating bunches could have different work points– And others…

Some theory

• Electron lenses could be used to fight mentioned problems:– Right beam shape and intensity allows footprint compression– Fast modulation allows bunch to bunch adjustments of work point

Electron Lenses vs. Regular Magnet

Wider variety of field configuration

Yes No

Bunch to bunch strength adjustment

Yes No

Overall strength of field

Small Any

Gaussian profile vs. SEFT profile . Ability to compensate tune spread

Good Moderate

Ability to shift work point

Moderate Good .

r Gx(x,0) Gx(0,y)

x, y, r x, y, r

Other ways to use electron lenses• Abort gap cleaning (in use)

– By pulsing gun every 6 turn during the abort gaps, unwanted particles are eliminated by excitation of high order resonance.

• Halo cleaning (proposal)– By forming tube electron beam and

aligning it with treated one, it is probably possible to decrease the lifetime of halo particles, without affecting the core.

Plans• Gaussian gun

– Test profile quality– Install the gun into TEL2 instead of the SEFT one– Study the tune spread control ability theoretically – Study the tune spread behavior of the treated

beam

• SEFT gun– Install the gun into the test bench– Test profile quality– Look if we can adjust gun’s parameters to make

“hollow” profile

Outline of a Gun design

Anode

Control Electrode

Magnetic Field

Cathode

Filament

Impregnated cathodes

Tungsten BaO, …During activation, chemicals

from porous react and form a monoatomic layer of Ba. This layer is very fragile, and in case of destruction requires time consu-ming reactivation procedures.

Testing the guns: test benchGun

Gun solenoid

Vacuum chamber

Pickups and other electrodes

Collector

Profile meterCorrector solenoids

Main solenoid Collector solenoid

Tube

Testing the guns: perveances

Cathode needs activation after exposure to the air or even a long standing without filament current. For the Gaussian gun it took about a week. The SEFT gun didn’t fully restore after two weeks.

Testing the guns: Gaussian gun profile

Date: 19 Feb 2009Magnetic fields: 1-1-1 kGsFilament current: 4ACathode & Control electrode: -5kV

Testing the guns: Gaussian gun profile

• Date: 24 Feb 2009• Magnetic fields: 1-1-1 kGs• Filament current: 4.15 A• Cathode & Control electrode: -6 kV

Testing the guns: Gaussian gun

• Date: 27 Feb 2009• Magnetic fields: 3-3-3 kGs• Filament current: 4 A• Cathode & Control electrode: -6 kV

Testing the guns: SEFT gun

• Date: 8 Jul 2009• Magnetic fields: 1.5-1.5-1.5 kGs• Filament current: 6.7 A• Cathode & Control electrode: -0.5 kV

Solenoidal field profile

Field profile in TEL-2 main solenoid, at 439.4A, corrected with dipole correctors.

Theoretical tune spread

))/(1()(

40

eSEFT r

r

0

22

22

2

222

222

22

22 )(

/)(

)/)arctan((2),(

yx

yx

x

yx

yx

yx

xyyxv

e

exSEFTx

0

22

22

2

222

2222

22

22 )(

/)(

)2)(exp(12),(

yx

yx

x

yx

yx

yx

xyyxv

e

exGaussx

)2exp()( 220 eGauss rr

0,

2

1

cp

eLTELyxex

Since the length of the interaction region in the TELs is much smaller than beta-functions in its locations, then we can consider TELs as “short” elements. In this case, to model the imperfect aligning, one can split the simulated beam into several slices and summ the effects to model the influence.

Theoretical tune spread

Antiproton orbitElectron beam Slices

(0,y)

(x,0)

y

x

y

x

0,y)

0,x)

Sanity check for slicesTo check the quality of the sliced fit it is useful to look at

difference between this fit and numerical integral:

1 slice 2 slices 4 slices3 slices 5 slices+-1pitch

Gaussian profile

)0,0(

d))(),((1

),(1

),( 0

,,

G

ssyysxxGL

yyxxGN

yx i

L

eeTEL

isliceisliceslices

TEL

SEFT profile

104 particles with gaussian distribution

Theoretical tune spread

Gauss SEFT

y

x

y

x

Tune spread compensationGauss SEFT

y

x

y

x

• Perfect alignment• Amount of compensation: from 0% to 150%

Tune spread compensation: symmetrical tilt in X-Z plane scan

Gauss SEFT

• Full compensation.• xi varied from 0 to -3• xf varied from 0 to 3• yi = 0, yf = 0

y

x

y

x

Tune spread compensation: symmetrical tilt in XY-Z plane scanGauss SEFT

y

x

y

x

• Full compensation.• xi, yi varied from 0 to -2• xf, yf varied from 0 to 2

Tune spread compensation: shift in X-Z plane scan

Gauss SEFTy

x

y

x

• Full compensation.• xi, xf varied from 0 to 2• yi = 0, yf = 0

Tune spread compensation: symmetrical tilt in X-Z plane scan

Gauss SEFTy

x

y

x

• Half compensation.• xi varied from 0 to -3• xf varied from 0 to 3• yi = 0, yf = 0

Tune spread compensation: symmetrical tilt in XY-Z plane scanGauss SEFT

y

x

y

x

• Half compensation.• xi, yi varied from 0 to -2• xf, yf varied from 0 to 2

Tune spread compensation: shift in X-Z plane scan

Gauss SEFTy

x

y

x

• Full compensation.

• xi, xf varied from 0 to 2s

• yi = 0, yf = 0

Final choice: 1/3 of strength

Perfect alignment

X shift 0.5

X Pitch +-2 X&Y Pitch +-2

X shift 1 XY shift 0.5

BPMs of the TEL2

• One bad channel with strong reflections• Frequency dependence

– Different calibrations and different offsets for (anti)protons and electrons

Switch

Scope

A BPC

GPIB

ACNET

Algorithm for new program• Determine and subtract offset, using first N points

or whole sample.• Find minimum and maximum in signals from both

plates– Find moving average extremums– Fit MA extremum region with parabola and find it’s

precise position• Shift signals to match the extremums• Determine the regions of high signal to noise ratio

– Points where absolute values of fitting parabolas grater then half of the corresponding extremum

• Take average of (A-B)/(A+B) from points in the selected region

New Java based soft for BPMsInitialization of oscilloscope

and switch

Select appropriate channel with the switch

Set up timing for desired channel and particles’ type

Collect binary data from the oscilloscope

Treat the data in any way

Display result

Send data to the ACNET

Infinite loop

Conclusion

• Sensitivity of tune spread compensation to alignment of proton and electron beams was studied with analytical model.– Maintaining shift of less than 0.3 is critical.

• It is possible to partially compensate “gaussian” tune spread with SEFT electron beam.

• Gaussian gun was tested and installed in the TEL2• New java-based software for the BPMs on TEL2

was developed, but not fully tested because of shutdown.