1. 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

2. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 2 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

3. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 3 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

4. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 4 Injection/Extraction Layout Harmonic RF Injection/Extraction System Injected Bunch Extracted Bunch Injection Septum Extraction Septum

5. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 5 Example h = 6 Kick X X X X XXX X XXX X Ring Linac

6. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 6 Inject/Extract One Bunch Every Six Bunches Use three sub-harmonics of bunch frequency and DC kick Solution provides required values at bunch positions

7. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 7 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

8. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 8 Field Variation Calculation by Reza Kazimi

9. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 9 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

10. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 10 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

11. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 11 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

12. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 12 CEBAF RF Separator

13. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 13 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

14. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 14 Driver for CEBAF RF Separators IOT with drive electronics Power supply for 4 IOTs

15. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 15 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

16. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 16 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

17. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 17 Harmonic Number of Circulator Ring If the harmonic number of the circulator ring H c 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 H c Easiest choice h = 16, and H c 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 H c should be about 6000

18. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 18 Harmonic Number of Circulator Ring (cont) Harmonic number H c should be divisible by many factors At a minimum 3, 5, 7 H c should be divisible by 105 Good options are: H c Circumference (3x5x7)x7x7= 51451031 m (3x5x7)x3x17= 5355 1073 m (3x5x7)x53= 55651115 m (3x5x7)x5x11= 57751157 m (3x5x7)x3x19= 59851199 m (3x5x7)x59= 61951241 m (3x5x7)x61= 6405 1284 m (3x5x7)x3x3x7 = 66151326 m

19. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 19 Example Assume h = 16, H c = 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

20. Operated by the Southeastern Universities Research Association for the U.S. Department of Energy Thomas Jefferson National Accelerator Facility Page 20 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