1. Shuichi Noguchi, KEK6-th ILC School, November 20111 Beam-Operation Cavity Voltage Control by Feedback & Tuner Dumping of HOM’ ｓ by HOM Dumper  Bunch Induced Voltage  Beam Loading  Higher Order Mode Excitation

2. Shuichi Noguchi, KEK6-th ILC School, November 20112 RF Acceleration System P0P0 RF Signal Generator Frequency Fixed RF Amplifier Directional Coupler Circulator Cavity Phase Detector Pr P t ( V C ) Pg Pre-Amp. Phase Shifter Reference Phase Frequency Tuner Pre-Amp Reference Voltage

3. Shuichi Noguchi, KEK6-th ILC School, November 20113 Cavity Field Equation Drive Force ; RF Power Source & Beam Cavity Field is given by Superposition of RF Driven Field & Beam Induced Field

4. Shuichi Noguchi, KEK6-th ILC School, November 20114 Beam ( Bunch ) Induced Field V b,  U b Charge q L Cavity

5. Shuichi Noguchi, KEK6-th ILC School, November 20115 Energy Loss Mode Excitation

6. Shuichi Noguchi, KEK6-th ILC School, November 20116 How much Field is Induced ? Let’s Assume  Energy Loss to each mode is due to Deceleration by Self Induced Field.  Excitation of the Mode is Zero, If Two Bunches of Equal Charge apart by  Passed through the Cavity.

7. Shuichi Noguchi, KEK6-th ILC School, November 20117 Beam ( Bunch ) Induced Field  V b,  U b q

8. Shuichi Noguchi, KEK6-th ILC School, November 20118 V b1 ｆ V b1  U 1 = q f V b1 Reference Phase Energy Loss by Self Induced Field Bunch feels Fraction ( f ) of Self Induced Voltage exp ( j  beam t )

9. Shuichi Noguchi, KEK6-th ILC School, November 20119 Beam ( Bunch ) Induced Field  V b1,  U b1 Bunch 1 Bunch 2

10. Shuichi Noguchi, KEK6-th ILC School, November 201110 Beam ( Bunch ) Induced Field   U = 0 V b = 0

11. Shuichi Noguchi, KEK6-th ILC School, November 201111 V b2 ｆ V b2  U 2 = q ( f V b2 – V b1 ) Reference Phase V b1 exp ( j  beam t )

12. Shuichi Noguchi, KEK6-th ILC School, November 201112  U 1 +  U 2 = 0 qfV b1 + qfV b2 – qV b1 = 0 f = 1/2 ( or V b = 0 ) V b1 = V b2

13. Shuichi Noguchi, KEK6-th ILC School, November 201113 Multi-Bunch Induced Field VbVb exp ( j  beam t ) Phase Advance 

14. Shuichi Noguchi, KEK6-th ILC School, November 201114 CW Limit

15. Shuichi Noguchi, KEK6-th ILC School, November 201115 CW Limit

16. Shuichi Noguchi, KEK6-th ILC School, November 201116Shuichi Noguchi, KEKSokendai Lecture, 2011,216Shuichi Noguchi, KEKSokendai Lecture, 2011,216 exp ( j  RF t ) Phaser Diagram Beam Phase  O 

17. Shuichi Noguchi, KEK6-th ILC School, November 201117

18. Shuichi Noguchi, KEK6-th ILC School, November 201118

19. Shuichi Noguchi, KEK6-th ILC School, November 201119Shuichi Noguchi, KEKSokendai Lecture, 2011,219 exp ( j  RF t ) Another way to find Tuning Condition Beam Phase  O 

20. Shuichi Noguchi, KEK6-th ILC School, November 201120 ＢｙＴｕｎｅｒ

21. Shuichi Noguchi, KEK6-th ILC School, November 201121 exp ( j  RF t ) Phaser Diagram at Tuning Beam Phase O

22. Shuichi Noguchi, KEK6-th ILC School, November 201122

23. Shuichi Noguchi, KEK6-th ILC School, November 201123 Pulse Operation Drive a tuned cavity with a power

24. Shuichi Noguchi, KEK6-th ILC School, November 201124 ｔ V CW VgVg VbVb PgPg TeTe VCVC 0 TbTb Cancel

25. Shuichi Noguchi, KEK6-th ILC School, November 201125