Skip to content

Minutes of #6 Remote E-Beam Meeting

The meeting was held on Vidyo on 08/07/2020 - See indico

Participants

Adriana Rossi, Alessio Mereghetti, Ana Miarnau Marin, Danila Nikiforov, Davide Gamba, Giulio Stancari - FNAL, Martin Droba - University of Frankfurt, Ondrej Sedlacek, Ray Veness, Roberto Corsini


Introduction about Magnetic Design of the HL-LHC Hollow Electron Lens (HEL) (Adriana Rossi)

Changes:

  • 2 gun solenoids
  • collector solenoid (1 T for the time being)
  • Iron shield to improve quality of magnetic field and increase it in the gaps between solenoid.

Work ongoing

  • Ondrej:
    • WARP simulations to offer alternative and cross check CST simulations, plus find a WARPED meshing to reduce computational load
  • Ana:
    • see largest possible mesh size in CST to speed up calculation of magnetic field, knowing that once the ion shield is included, simulations will take a much longer time.
    • same for particle tracking

Future work

  • CST using ‘optimised’ mesh sizes
    • Calculate (with iron shielding) particle trajectory and correctors necessary to obtain smooth injection
    • Estimate correctors necessary for ‘realistic’ model (misalignments or LHC beam off orbit) and e-beam trajectory at main gap
    • Work out collector side (solenoid needed and collector design)
  • WARP:
    • Validate CST particle and energy distribution maps for calculations of HEL effect on LHC beam

Warp Simulation of electron transport (Ondrej Sedlacek)

Simulation of electron transport in the injection side of the HEL, including the gun, bend and first main solenoid, without correctors.

  • Magnetic field from magnets imported from CST
  • Magnetic self field neglected -> magnetostatic
  • High charge density -> high electric field and space charge is important
  • 3D Electrostatic PIC simulations (Poisson equation solved each time step) -> time step has to be small enough not to change E-field too quickly around particles
  • 3D PIC simulations
  • Using Warped Cartesian Fernet-Serre coordinates, i.e. Cartesian coordinates in the straight pipes and polar coordinate in the bend, (1.25mm mesh) -> to reduce the volume, number of mesh cells
  • Gun simulator from V. Moens CERN-THESIS-2013-126, scaled

Results

  1. Virtual cathode phenomenon (or Pierce's instability): As predicted by D. Nikiforov et al., if cathode biased to -10kV, and anode + beam pipe grounded (i.e. extraction voltage = accelerating voltage = 10kV), as e-beam is compressed, particles go back.
  2. If cathode biased to -15kV, anode at -5kV and pipe grounded (i.e. extraction voltage = 10kV and accelerating voltage = 15kV) electron can travel throughout the HEL structure.
  3. After the bent, the e-beam goes a bit below the circulating LHC beam axis (~ 1mm) = e-beam offset.
    • Trajectory spread for different simulations ~30 \mum.
    • Results are also in good agreement with CST.
    • Varying the anode-cathode voltage and therefore the e-beam current, does not affect the e-beam offset.
  4. Calculated self magnetic field ~ 0.1 Gauss to compare to a few Tesla HEL magnetic field, so justified to ignore it.
  5. Varying bending radius up to 45%:
    • no effect on trajectory, spread ~20\mum.
    • no evident effect on transverse particle distribution. The fact that the electron distribution is not perfectly round can be imputed to the fact that the mesh size is 1.25 mm against beam inner/outer diameters are ~2./4. mm, so the interpolation can cause some deformations.

Summary

Warp simulation constructed with usage of “Bent mesh”

  • Pipe and junction according to HEL design; (E-gun (scaled design of V. Moens))
  • Simulations tested:
    • Beam is magnetized and follows the magnetic field lines
    • Magnetic self-field neglecting in simulation seem justified.
    • Study of effect of mesh bending by varying the bending radius by up to 45% does not affect significantly the trajectory calculations or beam cross section profile
      • Beam offset unchanged with σ = 21µmm
      • No obvious bend radius dependent artifacts in beam profile
  • Beam offset
    • Seems independent of beam current with currents of 7, 5.2, 2.9 A producing σ = 31µmm
  • In good agreement with CST

Future steps

  • Comparison of particle and energy distribution to CST
  • Simulating without bent mesh to provide robust test of the mesh bending effect

Discussion

Giulio : which resources/how much time for a simulation? Ondrej: RAM ~100Gb, 40 threads of CPU ~20h per simulations to simulate 63 ns evolutions.

Giulio : e-beam transverse displacement at the bent could be estimated analytically from B X gradB

Adriana: a manual will be made available.

Martin: 1. Is the mesh cylindrically symmetric? 2. How large is the self electric field? Ondrej No. The typical E field of the beam few 100 keV/m to be compared to maximum accelerating field of 15 kV

Martin Check that B X B equals E X E, and check transport before and through the bend (E X B). The size of the cartesian mesh is comparable with the size of the e-beam and there is a linear approximation of the fields in a mesh cell. If we assume a cylindrical symmetry for particle distribution, there will be a difference between the numerical and the real E-self field, especially in one direction. In case of high E X B term (that is v_drift=E/B could be comparable with v_parallel), the real beam shape evolution would be different from what is estimated because of the differences between the numerical E-field direction and the real one. Similar to the B X grad(B) term, which was mentioned by Giulio before, you can estimate such beam motion analytically (estimation of the terms vect(B), grad(B) and vect(E) and the corresponding drifts).


CST PARTICLE STUDIO Mesh variation and impact on magnetic field and beam trajectory simulations (Ana Miarnau Marin)

Study effect of mesh in CST to find the right compromise between resources and time and accuracy of result obtained.

  1. Magnetic field calculations need to have a big enough boundary box to include return field lines: 3 simulations performed: chosen the smallest box when field did not change.
  2. Mesh size varied from 2, 2.05, 2.1, 2.2, 2.4 and 2.8 mm (called m-mesh).
    • Results plotted along median line of the beam pipe - magnetic field strength.
    • \Delta ~1 mT between m-mesh values of 2., 2.05. 2.1 and 2.4 mm, but 2.2 and 2.8 mm are further away. No specific pattern throughout.
    • The field oscillates by ~ 10 mT just after the BPM location, is that an artifact of the simulation or a real effect?
    • Inside the main solenoid, all results are comparable (\Delta ~0.2 mT)
  3. Use magnetic field results from step 2. (with different values of m-mesh). to then track electrons with minimum possible boundary box, and with 2 mm mesh size (hereby called t-mesh) (To be noted ~6 \mum difference with t-mesh varied between 1.6 mm and 2 mm).
    • Electrons follow the magnetic field lines, so there is no evident trend when using magnetic field calculated with different m-mesh sizes. Max \Delta ~ 400 \mum (to be compared to 300 \mum sigma beam). Inside the main solenoid better, since magnetic field difference lower.

Conclusion

  • field values do differ with no clear pattern of convergence

Electron beam simulation:

  • Smaller simulation box'
  • Visible small bump of about 1 mm (see Ondrej's presentation) going below central line.
  • Also not converging toward a limit value.
  • Maximum variation of e-beam position > 1 LHC beam sigma!

Discussion

Ray: 1. Would you have an idea on how this compares to the field variation deriving from production error of magnetic fields? i.e. are those error significant? 2. What happens between the 2 main solenoids? Adriana: a. We are requiring 10E-4 precision on magnetic field error, so this is significant. b. Simulation up to first main solenoid, but second is not included, so calculation of magnetic field correct only up to mid first solenoid (since it does not include the overlap of the fringe field of the second main solenoid). The electron source is non-physical, just a ring of electron emitted perpendicularly and all at the same energy, but is good enough for evaluating differences in trajectory due to t-mesh.

Giulio: 1. Mechanical tolerances and predicting beam trajectory < 100um is difficult. At the Tevatron straightness no better than 100 um and at RHIC > 50 um. 2. Accuracy studies: good to have a comparison with analytical case. 3. Have you tried CST mesh refinement? Ana: CST seems to like better uniform meshing in XWZ. But if there is time I will try. Giulio suggested to use two solenoids with axis at a given angle. The field at the intersection of the two axes can be calculated analytically.

Martin: Is the largest difference at beginning/end of BPMs? Actually first oscillation falls at the end BPM, then after the BPM. Maybe mesh size changes the actual geometry of the objects (i.e. whey they start/end).

Adriana to Danila: to make calculation you used which mesh size? -> BINP used Opera, will check with Alexei Barnyakov.

Ondrej: position of nearest mesh point with respect to position where you show might be different - the interpolation may lead to errors.


A.O.B. Debye length in a magnetised non-neutral plasma

Adriana: Debye length?! how to actually compute it for a magnetised non-neutral plasma? We wanted to calculated it and compare it to the mesh size to see if all physics is taken into account. Larmor radius for our case is of the order of 100 \mum. But we cannot got down to such a mesh size. So can we at least check how far we are from the Debye length. Martin: \lambda_{D} = \sqrt{\frac{\epsilon_0 k T}{ne^2}} Giulio: 1) The e-beam time of traveling between the cathode and the anode is of few/10 ns, it is never in thermal equilibrium, so temperature is not well defined. 2) The temperature of cathode doesn't matter, because the transverse temperature of a few eV, not at all in thermal equilibrium with the cathode for magnetised beams. 3) Longitudinal and transfer temperature are in general very different in these cases.

Ondrej: how to justify that it acts as a plasma? How to characterize it? Giulio: the ratio between the self electric field compared to external field, given the very large particle density. But it does not behave like a free plasma, because does not have enough time to get into thermal equilibrium and since it is strongly magnetised.

Giulio: General comments on this discussion, for reference. The importance of space charge can be characterized by the ratio of self fields and external fields or, similarly, by the ratio of plasma frequency and cyclotron frequency. See also Reiser, Theory and Design of Charged Particle Beams, pp. 163-165. On a related note, in Warp and other PIC codes, it is possible to choose time steps that are larger than the cyclotron period while preserving the trajectory of the centers of gyration and the drifts (ExB, B x grad B): https://doi.org/10.1016/j.nima.2007.02.035 http://warp.lbl.gov/home/how-to-s/particles/drift-lorentz