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Minutes of #4 Remote E-Beam Meeting (draft)

The meeting was held on Vidyo on 29/04/2020 - See indico

Participants

M. Ady, J. Cenede, D. Gamba, A. Mereghetti, D. Mirarchi, A. Mirinau Marin, D. Nikiorov, R. Kersevan, R. Jones, A. Pikin, A. Rossi, S. Sadovich, O. Sedlacek.

Simulation of electron transport within Hollow Electron Lens using Warp – Status report (O. Sedlacek)

The intent of the work of Ondrej is:

  • simulate electron beam transport in electron lenses (but eventually also cooling), in particular the bends.
  • Using WARP against CST for two reasons:
    • CST is more a "black box" where not all physics being implemented is known
    • WARP allows to simulate a bend-like object with a curved mesh, which is something that is not possible in CST.
      • this will give more precision to the results, and hopefully less demanding from a computational point of view.

Details on the simulation steps were given:

  • Beam is generated on the cathode surface according to Child-Langmuir law.
  • The charge density is interpolated over the grid of the chosen mesh.
  • Poisson equations are solved to get electrostatic field on the mesh.
  • The electric field is linear interpolated form mesh points to actual particle position
  • Time is advanced using "leap-frog" method.

Each figure presented in the slides is a snapshot at a given time of the tracked particles along the assembly being simulated.

The timeline of the study is:

  • Simulate the transport in a simple series of two solenoids, i.e. check that simulations agree with well know transverse compression formula.
    • This step has been successfully achieved.
  • Simulate the electron gun:
  • Simulate the first part of HEL, i.e. gun, bend, part of drift solenoid.
    • This part of the work is the one being investigated in details at the moment.

Details of the mesh were given. Using WARP coordinate, in the bend area one can define a defined radius along which to develop a mesh in polar coordinate and then go back to Cartesian coordinates. This, in principle, should not have any effect on the physics, but it allows for reducing considerably the mesh size. Ondrej underlined that the physics of the time advance in this area has to be studied to understand to understand if and which approximations are made.

Results from first simulations were been shown in details:

  • the electron been is nicely centered on the chosen mesh.
  • the beam follows the magnetic field lines, and the compression factor from gun to drift solenoid is as expected from the simple theoretical formula r_1/r_2 = \sqrt{B_2/B1}
  • WARP is not considering the electro-magnetic fields self-generated by the beam itself.
    • Ondrej computed the self-induced magnetic field at a given location for a typical beam, and found to be of the order of 1.5 Gauss weather the nominal magnetic field generated by the surrounding solenoids is order of 1 T. It is therefore deemed reasonable to neglect the self-generated field.
    • He also computed the self-induced electric field, which appears to be qualitatively consistent with what one would expects.
      • Note that the mesh step is 1.25 mm. One should probably check if this is small enough given that the e- beam size is of the order of 6 mm in radious.
  • A naive computation of the Debye length turns out to be of the order of 4 m which seems to be very big compared to the beam size under consideration.
    • Adriana mentioned that the computation is done assuming several simplifications that should be verified more in details.

The next steps of the study will be:

  • Simulation without bent mesh, i.e. using pure Cartesian coordinates, and verify that results don't change.
    • Davide suggested to also consider simulating still bended coordinates, but with different mesh radius: this could be less memory-demanding and easier to perform.
  • Characterize more in detail the beam (Temperatures, Debye length, etc.), and verify that there are no numerical artifacts by:
    • Fine-tune simulation parameters (mesh size, timestep, etc.)
    • Find approximated analytical cases to compare with
  • Compare results with CST simulations

Discussion

  • Alexander suggested to change the bending radius of the beam or the geometry of the vacuum chamber to have the beam more centered in the vacuum chamber.
    • Adriana commented that the vacuum chamber design as shown in the slides is not representative of the real vacuum chamber: in reality, the beam is already much better centered.
  • Alessio asked if in the simulations one already sees the effect of drift gap between two drift solenoids:
    • Ondrej replied for the time being simulations stop 30 cm inside the drift solenoid, still far from the gap.

AoB: in preparation of future presentation on HEL

Adriana announced that a joint E-BEAM+Collimation meeting will take place in the coming months, in which Daniele should present the status of his studies on the effect of the residual dipolar field on the circulating beam core.

  • Daniele commented that the study is quite advanced, but he needs inputs on the expected pulse-to-pulse stability. He mainly cares about the total dipolar kick amplitude stability and distribution.
  • Alexander commented that no such a study were performed for BNL, so he has no feeling about the size of such effects.
  • Adriana commented that the used modulator technology and by running the gun in saturation (wrt cathode temperature and perveance) the shot-to-shot stability should be extremely good.
  • Sergey reported that in some paper at BNL the pulse-to-pulse stability was observed to be better than 0.3% (on modulator voltage, apparently)
  • Danila commented that self field inside hollow beam strongly depends on the actual e- beam current and it is non-linear. If one is asking to have a sizable change of beam current from shot to shot, then this should be taken into account.
    • Daniele commented that at the moment the strategy will be to pulse the HEL always at the same e- beam current, as this turns out to be the most efficient way for tail depletion and is also easier to implement in the hardware.
  • Davide asked if one expects an effect from solenoid field stability. This could be simulated in WARP just randomly changing the field strength and see if there is any sizable effect.

After the discussion, it has been agreed to consider as starting point:

  • Gaussian distribution
  • 10^{-2} r.m.s. stability