Freq [GHz]Q0Q0 R/Q [Ω]±Voltage [kV] 2.07224187862.340.22...

download Freq [GHz]Q0Q0 R/Q [Ω]±Voltage [kV] 2.07224187862.340.22 2.08329155730.510.04 2.09903219379.724.04 3.0231018102114.01.43 3.27113743239.10.12 4.716412612713.00.02

of 12

  • date post

    05-Jan-2016
  • Category

    Documents

  • view

    214
  • download

    0

Embed Size (px)

Transcript of Freq [GHz]Q0Q0 R/Q [Ω]±Voltage [kV] 2.07224187862.340.22...

PowerPoint Presentation

Freq [GHz]Q0R/Q []Voltage [kV]2.07224187862.340.222.08329155730.510.042.09903219379.724.043.0231018102114.01.433.27113743239.10.124.716412612713.00.024.71714227061.640.194.770592930928.80.36Sum6.46Freq [GHz]Q0R/Q []Voltage [kV]2.0733219955.71.820.182.0990422092.79.583.973.0241618264.7112.391.433.2818113718.643. 100.503.516727157.20.200.03Total6.141.925 beam pipeLongitudinal cut-off: 4.697GHz (TM01)1.875 beam pipeLongitudinal cut-off: 4.822GHz (TM01)Sum with fine structure: 5.84Without beating: 0.57Sum with fine structure: 5.14Without beating: 0.55Reference:Requirement: 7e-4 peak to peakdp/p: 2.57e-3dp/p: 2.92e-3To suppress the SOMs, we further reduce the end cell length to /2. (beam pipe 1.925) Freq [GHz]Q0R/Q []Voltage [kV]3.25741588210.50.123.28081760273.81.13.30341526534.60.36Total1.64Sum with fine structure: 1.57Without beating: 0.24SOMsFreq [GHz]Q0R/Q []2.0719143130.0352.0976199190.071dp/p: 7.9e-4Shift the 3.2808 GHz mode 0.5 MHz away from the harmonic of the 9.14 MHz gives 0.57 kV total fluctuation, corresponding to 2.9e-4 dp/p.Modelwith slot1.875/2+101.925 /21.925 /2+10k// [V/pc]2.742.51.821.85k// 2.11G [V/pc]1.621.041.161.04k// SHOM [V/pc]1.121.460.660.81How these HOMs change with fixed tuners.2If we use 30 bunches instead of 31 bunches, the voltage from 3.2808 GHz mode changes to 0.47 kV, and the sum with fine structure changes to 0.55 kV, without beating it changes to 0.16kV.If we use 30 bunches and 31 bunches alternatively in the train, the voltage fluctuation will be (1.57+0.55)/2=1.06kV.If we shift the 3.2808 GHz mode 0.5 MHz away from the harmonic of the 9.14 MHz, the 30-bunch configuration gives 0.32 kV fluctuation, and the alternating configuration gives 0.45 kV fluctuation. They are both less than the 31-bunch configuration.3.2808 GHz HOM

EH

Why 30-bunch configuration and 31-bunch configuration are different?

123456Voltage with n bunches

131415161718

Voltage with n bunches

262728293031Voltage with n bunches

The reason is that 3.2808 GHz is 4.663 times of the 704 MHz .

If we consider a mode 0.67 times of the fundamental.A single bunch gives Cos[] voltage fluctuation:

Two bunches giveCos[]+Cos[-0.67*2]*UnitStep[-0.67*2]

And three bunches give Cos[]+Cos[-0.67*2]*UnitStep[-0.67*2]+Cos[-0.67*2*2]*UnitStep[-0.67*2*2]

The voltage fluctuation from this mode will get cancelled every three bunches.Due to the 0.004 times slip, It will not fully get cancelled every three bunches.

Backup slidesTo suppress the SOMs, we further reduce the end cell length to /2. Freq [GHz]Q0R/Q []Voltage [kV]3.25741588210.50.123.28081760273.81.13.30341526534.60.36Total1.64Sum with fine structure: 1.57Without beating: 0.24Slightly change the end cell length to /2+2. SOMsFreq [GHz]Q0R/Q []2.0719143130.0352.0976199190.071Freq [GHz]Q0R/Q []Voltage [kV]2.0721200170.160.022.0977211850.490.203.22141781781.50.423.28791415044.70.134.6766283043.740.03Total0.81Sum with fine structure: 0.73Without beating: 0.08dp/p: 7.9e-4dp/p: 3.7e-4Shifting this mode 0.5MHz away changes the voltage to 0.41 kVdp/p: 2.1e-4(31 bunches, beam pipe 1.925 for all models) Slightly change the end cell length to /2-2. Freq [GHz]Q0R/Q []Voltage [kV]2.0970204990.360.053.27271443030.40.163.34471739266.31.093.35211672115.30.204.6732287563.940.06Total1.57Sum with fine structure: 1.40Without beating: 0.25dp/p: 7.0e-4Modelwith slot1.875/2+101.925 /21.925 /2-21.925 /2+21.925 /2+81.925 /2+101.925 /2+12k// [V/pc]2.742.51.821.801.951.861.852.09k// 2.11G [V/pc]1.621.041.161.181.151.001.041.00k// SHOM [V/pc]1.121.460.660.620.800.860.811.09ModelFreq [GHz]Q0R/Q []Voltage [kV]/23.28081760273.81.1/2-23.27271443030.40.16/2+23.28791415044.70.133.34471739266.31.093.22141781781.50.42