Harmonic Bunch Injection/Extraction for the ELIC Circulator Ring

1. Harmonic Bunch Injection/Extraction for the ELIC Circulator Ring Andrew Hutton

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. 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. Injection/Extraction Layout Harmonic RF Injection/Extraction System Extraction Septum Injection Septum Injected Bunch Extracted Bunch

5. Example h = 6 X X X X X X X X X X X X Kick Kick Ring Linac Kick

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. 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. Field Variation Calculation by Reza Kazimi

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. 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. 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. CEBAF RF Separator

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. Driver for CEBAF RF Separators IOT with drive electronics Power supply for 4 IOTs

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. 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. 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

18. 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

19. 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

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