1 & 2 JUNE 2015 – LLRF – BEAM DYNAMICS WORKSHOP URIOT Didier What is taken into account in simulations LLRF – Beam dynamics Workshop

| PAGE 2 (Focused on longitudinal & TraceWin …) What is done ?What is done ? What is being done ?What is being done ? What should be done ?What should be done ? Summary

3 WHAT IS DONE (TRACEWIN) Transport: Done most of the time using field maps, Integrator: Four order Runge-kutta, Interpolation: quadratic, RF phase could be relative or absolute. Today simulations are very close to a realistic nominal linac. Imperfections (RF Phase & Amplitude) : Static and dynamics errors, Coupled or not, Randomly (Uniform or Gaussian) distributed or from a set of data, Defined, using a set of field maps, Coupling between φ & E errors can be included (ex: φ err = kφ*E rr ) (see also N. Pichoff presentation), Diagnostics: Beam phase & energy (absolue or relative to perfect machine) Including accuracy Transient behavior including LLRF (see JL Biarrotte presentation)

4 WHAT IS DONE (ERROR TYPES) Static errors : the effect of these errors is detected and corrected. The strategy of the correction scheme is established to correct these errors. Variation slow enough to be corrected by the correction scheme. Dynamic errors : these errors are not corrected. They are induced by the noise of the RF field or mechanical vibrations from the environment. The effect of these uncorrected errors is simulated by adding them after the correction of the static errors. The amplitudes of this defect is usually one order of magnitude lower than the static errors. Variation too fast to be corrected by the correction scheme. Static errors : the effect of these errors is detected and corrected. The strategy of the correction scheme is established to correct these errors. Variation slow enough to be corrected by the correction scheme. Dynamic errors : these errors are not corrected. They are induced by the noise of the RF field or mechanical vibrations from the environment. The effect of these uncorrected errors is simulated by adding them after the correction of the static errors. The amplitudes of this defect is usually one order of magnitude lower than the static errors. Variation too fast to be corrected by the correction scheme.

5 WHAT IS DONE (APPLIED ERRORS) First order: Set cavity RF phase and field amplitudes Set beam transverse centroids (steering & BPM) Second order Transverse beam tuning (beam sizes, emittances…) Longitudinal beam tuning (Phase spread, energy dispersion…) First order: Set cavity RF phase and field amplitudes Set beam transverse centroids (steering & BPM) Second order Transverse beam tuning (beam sizes, emittances…) Longitudinal beam tuning (Phase spread, energy dispersion…) static Dynamic Main issues (RF) : Defined the error amplitudes. Make distinction between static and dynamics errors. Main issues (RF) : Defined the error amplitudes. Make distinction between static and dynamics errors.

First order: Set cavity RF phase and field amplitudes Set beam transverse centroids (steering & BPM) Second order Transverse beam tuning (beam sizes, emittances…) Longitudinal beam tuning (Phase spread, energy dispersion…) First order: Set cavity RF phase and field amplitudes Set beam transverse centroids (steering & BPM) Second order Transverse beam tuning (beam sizes, emittances…) Longitudinal beam tuning (Phase spread, energy dispersion…) 6 WHAT IS DONE (APPLIED ERRORS) Missing in TW simulation Consequence: RF errors are almost dynamic static Dynamic In transverse (alignment), the correction scheme compensates at a given position the consequences of the errors on the beam. In longitudinal the correction scheme (cavity tuning) cancels the errors themselves in the cavity. In transverse (alignment), the correction scheme compensates at a given position the consequences of the errors on the beam. In longitudinal the correction scheme (cavity tuning) cancels the errors themselves in the cavity.

7 If all RF errors are dynamic the longitudinal transport diverges very quickly. It’s acceptable for short machine such as spiral2, IFMIF, but not, for longer such as MYRRAH or ESS. Partial solution : The command, SET_BEAM_PHASE_ERROR, cancels beam phase errors coming from static errors. Then you have to put it regularly along your structure (objective: Don’t accumulate phase errors due to time of flight) - It’s not true for beam energy It’s complex to implement, it doesn’t work very well and this method doesn't correspond at all to reality. Finally, phase and amplitude RF errors are defined (ex: 1%, 1°) - But which part of the full RF system is concerned (LLRF, cavity, diagnostics …) ? - Which fraction distributed to which device ? WHAT IS DONE (ESS EXAMPLE)

8 Objective: improve the longitudinal beam dynamics simulation methods, by including more close-to-real models for the cavities tuning procedure.  By this way, clear distinction should be done between static and dynamic errors. Objective: improve the longitudinal beam dynamics simulation methods, by including more close-to-real models for the cavities tuning procedure.  By this way, clear distinction should be done between static and dynamic errors. WHAT IS BEING DONE + - Reference RF input Power supply Cavity Output antenna  LLRF  static = 1%, 1°  LLRF = dynamics (LLRF stability + Thermic phase shift in cable + beam loading…) Feedforward ?  static = 1%, 1°  LLRF = dynamics (LLRF stability + Thermic phase shift in cable + beam loading…) Feedforward ?  static

9 Objective: improve the longitudinal beam dynamics simulation methods, by including more close-to-real models for the cavities tuning procedure.  By this way, clear distinction should be done between static and dynamic errors. Objective: improve the longitudinal beam dynamics simulation methods, by including more close-to-real models for the cavities tuning procedure.  By this way, clear distinction should be done between static and dynamic errors. WHAT IS BEING DONE + - Power supply Cavity Output antenna Tuning procedure Beam diagnostics Reference set point (RF Phase and field amplitude  diag  LLRF  static = 1%, 1°  LLRF = dynamics (LLRF stability + Thermic phase shift in cable + beam loading…) Feedforward ?  diag = diagnostic accuracy  static = 1%, 1°  LLRF = dynamics (LLRF stability + Thermic phase shift in cable + beam loading…) Feedforward ?  diag = diagnostic accuracy  static

10 WHAT IS BEING DONE (SPIRAL2 EXAMPLE)  LLRF = dynamics (0.05%, 0.05°) TOF accuray:  W/W =  diag = 0.3% No static error has to be defined  LLRF = dynamics (0.05%, 0.05°) TOF accuray:  W/W =  diag = 0.3% No static error has to be defined  diag + - Power supply Cavity Output antenna Tuning procedure Beam diagnostics Reference set point (RF Phase and field amplitude  LLRF LLRF Spiral2 test performed on β=0,07 cryomodule on the cryogenic test stand at CEA/Saclay

11 RF tuning process: Based on beam energy measurement, RF power amplitude/phase will be chosen so that the energy and the phase signature match the theoretical ones, Implies to be confident to theoretical field maps, Implies to be able to detune cavity, Beam loading has to be canceled by cavity detuning. RF tuning process: Based on beam energy measurement, RF power amplitude/phase will be chosen so that the energy and the phase signature match the theoretical ones, Implies to be confident to theoretical field maps, Implies to be able to detune cavity, Beam loading has to be canceled by cavity detuning. WHAT IS BEING DONE (SPIRAL2 EXAMPLE, TUNING PROCEDURE) Cavity # being tuned Cavity detuned BMP1 BMP2 (t 2 –t 1 )/d Beam energy measurement, v = (t 2 –t 1 )/d Calculated energy, W(φ) Measured energy, W(φ) RF Phase W input Required energy s*s* Beam loading at 5 mA Successfully used on Linac4

12 WHAT IS BEING DONE (SPIRAL2 EXAMPLE, FIRST RESULTS) RMS for 1°, 1% Worse case for 1°, 1% Worse case for TOF = 0,3% RMS for TOF = 0,3% Preliminary tests for SPiral2 linac, first section from (0,75 MeV to 10 MeV, 12 QWR) First conclusions : Some instabilities due to off axis beam Tuning algorithm has to be improved, but it can be check 1 %, 1° were pessimistic First conclusions : Some instabilities due to off axis beam Tuning algorithm has to be improved, but it can be check 1 %, 1° were pessimistic 1000 linac

13 WHAT SHOULD BE DONE My proposal: It is easier to simulate the reality rather to find out a way or a model to simplify it. Linac designer: Defined cavity tuning methods, Diagnostics needed and corresponding accuracy. LLRF team: Defined the LLRF stability and extra errors, Defined coupling between phase and amplitude if it’s required. Code developer: Integrate cavity tuning procedures, Implement a way to set coupling between phase and field amplitude dynamic errors (Perhaps, randomly set the errors in a 2D area ?).

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