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

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Shuichi Noguchi, KEK6-th ILC School, November 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

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

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

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

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Shuichi Noguchi, KEK6-th ILC School, November 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.

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Shuichi Noguchi, KEK6-th ILC School, November Beam ( Bunch ) Induced Field V b, U b q

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Shuichi Noguchi, KEK6-th ILC School, November 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 )

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Shuichi Noguchi, KEK6-th ILC School, November Beam ( Bunch ) Induced Field V b1, U b1 Bunch 1 Bunch 2

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Shuichi Noguchi, KEK6-th ILC School, November Beam ( Bunch ) Induced Field U = 0 V b = 0

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

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

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Shuichi Noguchi, KEK6-th ILC School, November Multi-Bunch Induced Field VbVb exp ( j beam t ) Phase Advance

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Shuichi Noguchi, KEK6-th ILC School, November CW Limit

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Shuichi Noguchi, KEK6-th ILC School, November CW Limit

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Shuichi Noguchi, KEK6-th ILC School, November Shuichi Noguchi, KEKSokendai Lecture, 2011,216Shuichi Noguchi, KEKSokendai Lecture, 2011,216 exp ( j RF t ) Phaser Diagram Beam Phase O

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Shuichi Noguchi, KEK6-th ILC School, November

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Shuichi Noguchi, KEK6-th ILC School, November

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Shuichi Noguchi, KEK6-th ILC School, November Shuichi Noguchi, KEKSokendai Lecture, 2011,219 exp ( j RF t ) Another way to find Tuning Condition Beam Phase O

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Shuichi Noguchi, KEK6-th ILC School, November ＢｙＴｕｎｅｒ

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

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Shuichi Noguchi, KEK6-th ILC School, November

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

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

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Shuichi Noguchi, KEK6-th ILC School, November

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