Co-linear Two Beam Acceleration Lee Carver Christmas Meeting Friday 19th December 2014 19/12/14 Lee Carver - Christmas Meeting

Lee Carver - Christmas Meeting 2014 - Overview Started with a trip to Las Vegas… Initiated by electron emission driven by the RF electric field directing towards the wall, where electrons can be accelerated to escape from the wall, and stimulate a breakdown event; Promoted at surface irregularities which are accentuated by stresses induced by pulsed heating due to surface RF magnetic fields. 19/12/14 Lee Carver - Christmas Meeting

Lee Carver - Christmas Meeting 2014 - Overview Then flew directly to Geneva (without any sleep) to give a talk at the CLIC Workshop at CERN. Briefly followed by a weekend skiing. Initiated by electron emission driven by the RF electric field directing towards the wall, where electrons can be accelerated to escape from the wall, and stimulate a breakdown event; Promoted at surface irregularities which are accentuated by stresses induced by pulsed heating due to surface RF magnetic fields. It was all downhill from there… Spent rest of year working on verifying co-linear two beam acceleration principles, and working on longitudinal stability. 19/12/14 Lee Carver - Christmas Meeting

I.I Cavity detuning for collinear acceleration Monopole Mode Detuning Detuned cavities allow for collinear beams Phase shift, Tan(ϕ)= -2Qδ causes drive bunch to see low decelerating field. Test bunch phased to arrive π/2 later, sees high accelerating field. Transformer Ratio, T is the ratio of test bunch field to drive bunch field, T>>1 Can be shown that T = -2Qδ for unloaded case, Q is the cavity quality factor, δ is the magnitude of detuning. Verification needed between theory / eigenmode and time domain simulations. 19/12/14 Lee Carver - Christmas Meeting

I.II - Beam Excitation: Detuned-Cavity Two-Beam Accelerator Fixed Detuning Cavity period Λ +∆F Alternative Detuning +∆F -∆F A novel cavity configuration embodies most of the properties sought for the ideal two-beam accelerator, including the following: The cavity is an all metallic structure. No transfer or coupling structures are needed between the drive and acceleration channels. The cavity fields are symmetric around the axes of the drive beam and the accelerated beam. The structure can exhibit a high transformer ratio . Every other cavity, detuning flips sign Details in “High-gradient two-beam accelerator structure”, S. Yu Kazakov, S.V. Kuzikov, Y. Jiang, and J. L. Hirshfield, PRSTAB 13, 071303 (2010) Slide courtesy of Y.Jiang 19/12/14 Lee Carver - Christmas Meeting

Lee Carver - Christmas Meeting t3p Simulation Using the NERSC supercomputers, have used the ACE3P suite to simulate a cavity excited off resonance by a drive train. Can extract origin and surface fields to analyze. To calculate T, the drive bunch offset is calculated, and a Gaussian representing the drive bunch is integrated throughout the field and the energy gain is determined. Then an artificial (because it wasn’t in the actual simulation) Gaussian representing the test bunch is sent in 1/4fd later. T is calculated as the ratio of the energy gain by test bunch to energy lost by drive bunch. Excellent agreement is found, for example: Eigenmode T=9.318 Time domain T=9.321 19/12/14 Lee Carver - Christmas Meeting

Lee Carver - Christmas Meeting t3p Simulation Surface fields can be extracted for each time step from steady state field. Peak surface field for all time values is calculated and this time step is compared to eigenmode. Time Domain: Es,max /E0 =4.50736 Hs,max /E0 =0.008677 [μA/V] Frequency Domain: Es,max /E0 =4.68947 Hs,max /E0 =0.008689 [μA/V] 19/12/14 Lee Carver - Christmas Meeting

Multi-Harmonic Cavities Anode-Cathode Effect Design a cavity where the fields pointing into the cavity walls are smaller than fields pointing away. This can be achieved using the fundamental TM010 mode + an additional mode that can be either TM020/030/011/012, as long as the modes frequency is an integer multiple of the fundamental frequency. This is known as the anode-cathode effect. By increasing the potential for an electron on the surface of the material, it could inhibit field emission and prevent the onset of breakdown. Experiments being planned to prove/disprove this claim. Initiated by electron emission driven by the RF electric field directing towards the wall, where electrons can be accelerated to escape from the wall, and stimulate a breakdown event; Promoted at surface irregularities which are accentuated by stresses induced by pulsed heating due to surface RF magnetic fields. Potential energy u of an electron near the surface of a metal with x the distance of electron from surface. 19/12/14 Lee Carver - Christmas Meeting

Multi-Harmonic Cavities Pulsed Surface Heating Reduction May lower the pulsed surface heating. The superimposition of two harmonically related modes can lower the average H2 field on the surface. (Ideal pillbox η=H2max/H1max=2) Initiated by electron emission driven by the RF electric field directing towards the wall, where electrons can be accelerated to escape from the wall, and stimulate a breakdown event; Promoted at surface irregularities which are accentuated by stresses induced by pulsed heating due to surface RF magnetic fields. 19/12/14 Lee Carver - Christmas Meeting

Longitudinal Stability – Multi Mode Has it been done before? Multi-harmonic systems in use at ELETTRA (third harmonic) and for the PS Booster (second harmonic). They are used to flatten the seperatrix which can increase beam quality. The main difference is that they are additional cavities, each one operating in TM010. PS Booster Intensity Profiles – Top: Single, Middle: 1+2: Bottom: 1+2+higher harmonic Initiated by electron emission driven by the RF electric field directing towards the wall, where electrons can be accelerated to escape from the wall, and stimulate a breakdown event; Promoted at surface irregularities which are accentuated by stresses induced by pulsed heating due to surface RF magnetic fields. ELETTRA - Third Harmonic 19/12/14 Lee Carver - Christmas Meeting

Longitudinal Stability – Multi Mode Second Harmonic cavity: TM010+TM011 φz1,zh,n1=0, φsh=hφs1 Set α=0.222 (typical value for second harmonic cavity). Vary relative phase between the two modes. Etotal ΔW Initiated by electron emission driven by the RF electric field directing towards the wall, where electrons can be accelerated to escape from the wall, and stimulate a breakdown event; Promoted at surface irregularities which are accentuated by stresses induced by pulsed heating due to surface RF magnetic fields. φ 19/12/14 Lee Carver - Christmas Meeting

Longitudinal Stability – Multi Mode Third Harmonic cavity: TM010+TM012 φz1,n1=0, φzh,nh=π/2, φsh=φs1 Vary α while keeping gradient constant. Etotal ΔW Initiated by electron emission driven by the RF electric field directing towards the wall, where electrons can be accelerated to escape from the wall, and stimulate a breakdown event; Promoted at surface irregularities which are accentuated by stresses induced by pulsed heating due to surface RF magnetic fields. φ 19/12/14 Lee Carver - Christmas Meeting

Lee Carver - Christmas Meeting 2015 A few simulations still to do for thesis (multi-harmonic detuned accelerating cavities). Need to finish thesis. Start fellowship at CERN. Initiated by electron emission driven by the RF electric field directing towards the wall, where electrons can be accelerated to escape from the wall, and stimulate a breakdown event; Promoted at surface irregularities which are accentuated by stresses induced by pulsed heating due to surface RF magnetic fields. 19/12/14 Lee Carver - Christmas Meeting