Multiple Tune Jumps to Overcome the Horizontal Depolarizing Resonances

Haixin Huang

Spin 2014

Peking University

October 22, 2014 1

2

AGS as RHIC Polarized Proton Injector

AGS has been running as RHIC polarized proton injector with dual

partial snakes and two horizontal tune jump quads. It has delivered

~70% polarization with ~2*1011/bunch intensity with 80% as input

polarization.

AGS

BOOSTER

Pol. H- Source

200 MeV Polarimeter

AGS pC CNI Polarimeter

Cold Helical Partial Snake

Warm Helical Partial Snake

To RHIC Injection

Gg= 4.5 … 45.5

Gg= 2.2... 4.5 Jump quads in adjacent super-periods I &J

3

Simulation of Horizontal Intrinsic Resonances

• Vertical intrinsic resonances and imperfection resonances have been avoided by

introducing two partial snakes in the AGS. But the partial snake magnets also move

the stable spin direction away from the vertical and consequently excite depolarizing

resonances associated with horizontal tune, so-called horizontal intrinsic resonances.

They are driven by vertical oscillating fields (horizontal focusing) with horizontal

stable spin direction from partial snake

• For 10% and 5.9% partial snakes and 15 horizontal emittance polarization

transmission is predicted to be 91% in beam center (red), 83% for average (blue)

F. Lin, et al, PR. STAB 10, 044001(2007).

0 10 20 30 40 500.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

11

0.8

PHC10n

PH10n

45.280. Ggh n( )

Evidence of Horizontal Resonances from Polarization Profile

3 2 1 0 1 2 30.5

0.6

0.7

0.8

0.9

1

1.11.1

0.5

P1 82 x 10 1 ( )

w2

w2 w3

w2 w3

P2 82 x 20 2 ( )

v2

v2 v3

v2 v3

3.3. x q1 q1 q1 x u1 u1 u1

Polarizatio

n

Target Position (mm)

15% Cold Snake

10% Cold Snake

4 3 2 1 0 1 2 3 40

2 105

4 105

6 105

0.7 106

33.586

f1 x( )

w5

w5 w6

w5 w6

f2 x( )

v5

v5 v6

v5 v6

44 x q1 q1 q1 x u1 u1 u1Target Position (mm)

Normalize

d

Rate

15% Cold

Snake

10% Cold

Snake

The horizontal resonance effect is measurable over the whole ramp.

The following snake setup gave the best polarization: 10% cold snake,

5.9% warm snake.

Beam Profiles

Polarization Profiles

4

5

Horizontal Tune Jump

Change of nx is 0.04 in 100 ms. This increases the crossing speed in about 4 times.

Maintain the adiabaticity is the key to minimize any emittance growth even

for the benign tune jump.

12 20

2

ePPf

For an isolated resonance,

n

g

d

d

d

Gd

And resonance

crossing rate is

given by:

6

Chromaticity on the Ramp

7

Resonance Crossing (Gγ=36+νx=44.7)

To benefit from the tune jump, the beam particles have to cross the resonance line during the

jump. For the given beam parameters (tune jump amplitude, chromaticity, beam momentum

spread), about 76% beam will benefit from the tune jumps above Gγ =19.

8

Resonance Crossing (Gγ=54-νx=45.3)

9

Resonance Crossing (Gγ=17-νx=9.3)

The black dashed lines includes 76% of the total beam. More beam

benefit from the jump than higher energy cases.

10

Measured Betatron Tune along Ramp with JQ on

11

Three Issues with Tune Jump Quads On

• First one is the vertical emittance growth when both

jump quads on. The vertical beta functions at the

locations of both quads have to be equal to avoid

emittance growth. A horizontal 6th harmonic was

introduced during the run to minimize the beta beating.

• Over time, the orbit could drift away from the quad

center. An orbit feed forward system based on 9th

harmonics were used.

• The energy of beam has to be known along the ramp

accurately so that the jump quad timing can be driven

correctly(82 jumps). We are talking about ~100ms

accuracy for 82 times.

12

Vertical Emittances with Jump Quads on

Energy ramp finishes

13

Overall Jump Quad Timing Scan

Gaussian fit gives σ=214μs

H. Huang, et al, PR. STAB 17, 081001(2014).

14

Summary • The introduction of partial snakes generates horizontal intrinsic

resonances. They are generally weak but could cause accumulated

polarization loss if left uncorrected.

• A modest horizontal tune jump system has been used to overcome

these weak but numerous resonances while maintaining the

transverse emittances. A relative gain of 10-15% polarization has

been achieved with the tune jump system.

• The keys for the system are the accurate control of the jump quad

timing and the elimination of any emittance growth.

• This scheme paves the way to use partial snakes to preserve

polarization in the medium energy synchrotrons without the concern

of losing polarization due to additional horizontal intrinsic

resonances.