harmonic bunch injection/extraction for the elic circulator ring

Thomas Jefferson National Accelerator Facility

Operated by the Southeastern Universities Research Association for the U.S. Department of Energy

Harmonic Bunch Injection/Extraction for the ELIC Circulator Ring

Andrew Hutton



Introduction

• 2.4 Amps of polarized electrons are required to reach the ultimate luminosity in the ELIC proposal

• It is generally felt that future electron guns may be able to produce up to around 100 mA of polarized electrons• Present record is about 300 µA

• Slava Derbenev proposed to get around this limitation by using a circulator ring in which the electrons would spend up to 100 turns before being energy recovered• However, no viable scheme has yet been proposed to

inject and extract electrons in the circulator ring• Harmonic injection/extraction provides a partial solution

to the problem based on existing hardware• Could be implemented today



Concept

Concept assumes single bunches accelerated at a uniform, low repetition rate• Repetition rate is 1497/h MHz • Example is the 31.2 MHz G0 beam (=1497/48 MHz)

• Several RF separator cavities at different frequencies are used to extract one bunch every h bunches and re-inject a replacement bunch • Harmonic number of circulator ring should have no

common factor with h• Every bunch in the ring will be replaced every h

turns• Design for no kick on adjacent bunches

• Kick not required to be zero between bunches



Injection/Extraction Layout

Harmonic RF Injection/Extraction

System

Injected Bunch

Extracted Bunch

InjectionSeptum

ExtractionSeptum



Example h = 6

Kick Kick Kick

X X X X X X X X X X X X

Ring

Linac



Inject/Extract One Bunch Every Six Bunches

Use three sub-harmonics of bunch frequency and DC kick

• Solution provides required values at bunch positions

Sub- Frequency Kick Bunch Bunch Bunch Bunch Bunch Bunch Bunchharmonic MHz µrad 0 1 2 3 4 5 6

0 DC Kick 50 50 50 50 50 50 50 50

2 749 50 50 -50 50 -50 50 -50 50

3 499 100 100 -50 -50 100 -50 -50 100

6 250 100 100 50 -50 -100 -50 50 100

Total Kick Strength µrad 300 0 0 0 0 0 300



Inject/Extract One Bunch Every Twelve Bunches

• Use six sub-harmonics of bunch frequency plus a DC kick

• Solution provides required values at bunch positions• Solution is not perfect between bunches

Sub- Frequency Kick Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunchharmonic MHz µrad 0 1 2 3 4 5 6 7 8 9 10 11 12

0 DC Kick 25 25 25 25 25 25 25 25 25 25 25 25 25 25

2 749 25 25 -25 25 -25 25 -25 25 -25 25 -25 25 -25 25

2.4 624 50 50 -43 25 0 -25 43 -50 43 -25 0 25 -43 50

3 499 50 50 -25 -25 50 -25 -25 50 -25 -25 50 -25 -25 50

4 374 50 50 0 -50 0 50 0 -50 0 50 0 -50 0 50

6 250 50 50 25 -25 -50 -25 25 50 25 -25 -50 -25 25 50

12 125 50 50 43 25 0 -25 -43 -50 -43 -25 0 25 43 50

Total Kick Strength µrad 300 0 0 0 0 0 0 0 0 0 0 0 300



Field Variation

Calculation by Reza Kazimi



Inject/Extract One Bunch Every Sixteen Bunches

• Use eight sub-harmonics of bunch frequency plus a DC kick

Eight sub-harmonics is about the maximum that is reasonable

Sub- Frequency Kick Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunch Bunchharmonic MHz µrad 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0.0 DC Kick 50 20 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50

2.0 749 50 20 -50 50 -50 50 -50 50 -50 50 -50 50 -50 50 -50 50 -50 50

2.3 655 100 40 -92 71 -38 0 38 -71 92 -100 92 -71 38 0 -38 71 -92 100

2.7 561 100 40 -71 0 71 -100 71 0 -71 100 -71 0 71 -100 71 0 -71 100

3.2 468 100 40 -38 -71 92 0 -92 71 38 -100 38 71 -92 0 92 -71 -38 100

4.0 374 100 40 0 -100 0 100 0 -100 0 100 0 -100 0 100 0 -100 0 100

5.3 281 100 40 38 -71 -92 0 92 71 -38 -100 -38 71 92 0 -92 -71 38 100

8.0 187 100 40 71 0 -71 -100 -71 0 71 100 71 0 -71 -100 -71 0 71 100

16.0 94 100 40 92 71 38 0 -38 -71 -92 -100 -92 -71 -38 0 38 71 92 100

Total Kick Strength µrad 320 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 800



General Solution

• The exact solution is clear from these examples• Requires h/2 harmonically related RF frequencies

• Amplitude is equal for all except for 799.5 MHz which is half the amplitude

• Also requires a DC kick of half the amplitude

• The number of RF systems required goes up linearly with h• At some point, system becomes unmanageable• Also, total length of cavities must be small

compared to beta function at the cavities to maintain proper cancellation



Basis for Hardware Design

• Existing CEBAF RF separators• Five–pass separators work up to 6 GeV • They are designed to work up to 12 GeV

• Fifth-pass system uses three 499 MHz RF Cavities powered by a single IOT

• There are a total of four IOTs which are powered by a single power supply

Hardware solution for example of h = 6• 3 CEBAF RF separator-style cavities

• Each powered by a separate IOT• Frequencies are: 749,5 MHz, 499 MHz, 249.5 MHz

• One DC corrector



CEBAF RF Separator



RF Separator Cavities in CEBAF Tunnel

Three RF separator cavities are used to split 6 GeV beams in CEBAF

Separation is completed by downstream Lambertson septum magnet



Driver for CEBAF RF Separators

IOT with drive electronics

Power supply for 4 IOTs



Choice of h

• If h is small • Kickers are easier, fewer elements• Bunches stay only a few turns in ELIC

• Better for emittance degradation

• If h is large• Need many frequencies

• Many different RF systems• May also need matched sets of RF separators Π apart in

betatron phase to compensate residual kicks on adjacent bunches

• Easier for Injector• Gun current required = 2.4/h Amps



Optimum Value of h

• Maximum current in circulator ring 2.4 A• Maximum gun current (majority opinion) 100

mA

• Minimum value of h 24

• Maximum number of turns a bunch stays in circulator ring (emittance growth) 100

• Optimum value of h = 24-100

This proposal seems OK for h up to about 16



Harmonic Number of Circulator Ring

• If the harmonic number of the circulator ring Hc has no common factors with h, all bunches will be replaced in h turns

• This condition will be maintained if the number of bunches is a sub-harmonic of Hc

• Easiest choice h = 16, and Hc is odd (not divisible by 2)

• Circumference of circulator ring is about 1200 m• Wavelength at 1497 MHz is about 0.2 m

Harmonic number of ring Hc should be about 6000



Harmonic Number of Circulator Ring (cont)

• Harmonic number Hc should be divisible by many factors

• At a minimum 3, 5, 7 • Hc should be divisible by 105

• Good options are: Hc Circumference(3x5x7)x7x7 = 5145 1031 m• (3x5x7)x3x17 = 5355 1073 m• (3x5x7)x53 = 5565 1115 m(3x5x7)x5x11 = 5775 1157 m• (3x5x7)x3x19 = 5985 1199 m• (3x5x7)x59 = 6195 1241 m• (3x5x7)x61 = 6405 1284 m(3x5x7)x3x3x7 = 6615 1326 m



Example

• Assume h = 16, Hc = 5775

• Possible bunch spacings• 1, 3, 5, 7, 11, 15, 21, 25, 33, 35, etc

• Linac bunch frequency (MHz)• 1497, 499, 299, 214, 136, 100, 71.3, 59.9, 45.4, 42.8,

etc• Number of bunches in circulator ring

• 5775, 1925, 1155, 825, 525, 385, 275, 231, 175, 165, etc

• All bunches in the ring are replaced every 16 turns

• This layout preserves flexibility for commissioning and operating options



Summary

• Harmonic RF injection/extraction is a reasonable option up to about h = 16

• To first order, circulating bunches see no net kick• Second order effects come from total cavity length

• If the ring circumference is chosen wisely, there are many options for commissioning using same (or simpler e.g. h = 8) injection/extraction scheme

• Designed around existing CEBAF extraction system with cavities and power sources scaled to different frequencies• Another option might be a single (or a few) non-

resonant structure(s) fed by multiple frequencies simultaneously from a wideband amplifier

• Good topic for engineering design effort

harmonic bunch injection/extraction for the elic circulator ring

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