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Minutes of #2 Remote E-Beam Meeting (draft)

The meeting was held on Vidyo on 01/04/2020 - See indico


Status of SixTrack implementation for Hollow Electron Lenses (A. Mereghetti)

Alessio presented the status of the development of SixTrack in order to be able to correctly simulate the effect of Hollow Electron Lenses (HEL) on circulating beam. The material presented here was also presented at a recent informal review at CERN of the HL-LHC HEL magnetic design (ColUSM #122).

The HEL working principle is to deplete the content of beam tails above e.g. 3.5 beam sigma (assuming 3.5 mum normalised emittance). For HL-LHC beams it is expected that those tails could represent up to about 35 MJ stored energy. The presentation was focused on the code implementation rather then the physics results obtained so far. For the latter, Alessio suggests to look at D. Mirarchi contribution to the 9th HL-LHC Annual Meeting indico.

D. Mirarchi commented that:

  • In the past, mainly dynamic aperture reduction studies were performed.
  • Now studying:
    • simulations of rate of halo depletion - could be presented at a joint E-BEAM-ColUSM meeting
    • effect of the HEL on the core of the circulating beam, which is expected to be mainly a dipolar kick:
      • by bends used to guide in/out the electrons
      • by the residual field of the hollow electron beam
        • the S shape of HEL should compensate for those kicks, unless there are asymmetries
    • for the time being, only studying the maximum acceptable kick
      • when full field map will be available, it will be possible to quantify all effect independently.

Alessio continued explaining that the HEL is simulated as an ideal, indefinitely long column of cylindrical symmetric electrons, as done in other state-of-art tracking codes. On the other hand, with respect to the previous implementation (M. Fitterer et al.):

  • it is possible to simulate different radial profiles of electron beam - including full (i.e. not hollow) lenses
  • the HEL kick can be applied to all species of tracked particles
  • the full 6D closed orbit calculation can take into account the kick imparted by the HEL
  • the user interface has been made more flexible and the fortran module is fully dynamically allocated in RAM

A physics guide of the present implementation is being finalised.

The module of the ideal HEL does not allow to simulate border effects and imperfections of the HEL electron beam. To do so, a brand new SixTrack module has been developped which implements kicks of highly non-linear fields in a general manner. The implementation is based on the use of Chebyshev polynomials, the coefficients of which are obtained from fits to 3D maps of electric field and potential. The method has been described G. Stancari (FERMILAB-FN-0972-APC) for implementation in LifeTrack. The principle is based on:

  1. the use of numerical simulations to define distribution of electrons and compute the electric potential and field thus generated as 3D maps;
  2. the longitudinal integration of the maps, to get the integrated values – from 3D maps to 2D maps;
  3. the fitting through the 2D maps by means of Chebyshev polynomials – from 2D maps to fit coefficients;
  4. finally, the actual deployment of the fit coefficients in tracking code, to estimate effects of integrated fields on proton beam.

Maps of Chebyshev polynomials are symplectic by construction. This method is being applied to the present HEL design:

  1. 3D maps of electric field and electric potential generated by D. Nikiforov with CST (100 um mesh);
  2. Longitudinal integration (along circulating beam path) of the map and fit with Chebyshev polynomials by A.Mereghetti using numpy;
  3. Obtained Chebyshev polynomials will be plugged into SixTrack to see the effect in tracking simulations;

Alessio described the present 3D maps provided by D. Nikiforov; he pointed out some problems with the maps, which make their use questionable. Discussions are on-going with the Russian colleagues. The maps reflect the electron beam orbit shift at the entrance and exit of the main solenoids already investigated by A. Rossi (See E-beam, #1 remote WG meeting) and D. Nikiforov (See ColUSM #122). It was also possible to estimate the total kick affecting the circulating beam (at 7 TeV) to be of the order of a few nrad, which is consistent with previous studies by G. Stancari (FERMILAB-FN-0972-APC).

Alessio also showed the quality of the fit of the provided maps with Chebyshev polynomials. The obtained Chebyshev coefficients can be used in SixTrack simulations. Alessio underlines that the new module dedicated to Chebyshev maps is independent from the ideal electron lens model, such that this approach could be used for other effects (e.g. e-cloud). Note that at the moment this module is built to simulated electric fields (in this case, the electric field associated to the electrons). The possibility to also describe magnetic fields (which would be necessary for e-cooling studies, for example) is being considered, but not a priority for the time being.

Discussion

  • S. Sadovich asked if a 100 um mesh is necessary. Alessio replied that in the transverse plane it is, as the circulating beam size is of the order of 300 \mum sigma, while longitudinally this mesh could be relaxed indeed.
  • A. Pikin asked if the simulation of the electron beam transport takes into account or show the effect of possible diocotron instability. Alessio replied that he cannot conclude from the maps that the instability is included. The current priority tracking simulations of the main beam is to find optimal values for the main HEL parametners and to look at the leading effects that could act on the core of the circulating beam.
  • D. Gamba mentioned that one should also look at how RF-Track (by A. Latina) is treating similar problems where complex (and heavy) electro-magnetic field maps have to be treated in a simplified way for long tracking.
  • D. Gamba asked if this new SixTrack module could be used in the future for simulating e-cooling. Alessio replied that at the moment one important missing ingredient is the transfer of momenta from the circulating beam to the electrons, which is one of the key concept for e-cooling. However, Alessio does not see any big show stopper for extending the module to allow for cooling studies as well - if needed and if resources are allocated.