ANL-AAI-TN-2007-002

May 2007

**A BRIEF SUMMARY OF WORK ON ELECTRON**

**CLOUD EFFECTS**

Srinivas Krishnagopal

**[A brief summary of work on electron cloud effects]{.underline}**

Electron cloud studies are usually divided into two parts. The first is
to understand and model the growth of the electron cloud due to a given
drive beam and environment. The second is to understand the effect of
the cloud on the dynamics of the beam. Ideally, of course, one would
want to look at the self-consistent evolution of the cloud and the beam.

The code POSINST models the growth of the electron cloud in
accelerators, using detailed models of secondary electron emission. It
also takes into account space-charge effects, but does not model
evolution of the drive beam, under the influence of the electron cloud.
The environments that POSINST can model are: drift space and bending
magnet. We used POSINST to study two different sets of experiments.

**A. Simulations for APS**

We have used POSINST to model the set of experiments done by Kathy
Harkay at the APS. In this case studies were done in a drift space. Some
earlier simulations were done using an older version of POSINST, but
there were limitations to the code at that time. In particular, it was
then not possible to look at a limited part of the vacuum chamber --
i.e. just where the RFA was mounted.

> \(1\) Simulations show a difference between the old and new versions
> of POSINST, in the evolution of the cloud density with time. The
> origin of these differences is presently unclear, since, to the extent
> determinable, we are using identical input conditions.
>
> \(2\) We looked at the incident wall current as a function of bunch
> spacing. Over the range investigated, the behaviour is largely in
> agreement with experiment.
>
> \(3\) The electron wall flux as a function of energy is also roughly
> in agreement with experiment, though more simulations are needed for a
> closer look.
>
> \(4\) Simulations showed the interesting feature that at energies
> beyond around 10 eV, the secondary electron spectrum is dominated by
> the rediffused electrons. Previous simulations indeed showed a strong
> sensitivity to the input parameters that determine properties of the
> rediffused electrons, but such detailed output were not then
> available. This sensitivity needs to be better understood and can now
> be studied with the new version of the code.

With the new version of POSINST, the following issues can be studied by
simulation:

(a) How does the cloud picture change if you look at different places
    around the chamber, i.e. if the RFA were mounted at a different
    position?

(b) Study electron cloud distribution during buildup for both positron
    and electron beams and compare with RFA data. Resolve poor agreement
    for electron beams in previous simulations.

(c) Model RFAs near photon absorbers and compare with RFAs far away --
    the buildup and multipacting condition are experimentally very
    different.

(d) What is the role of resonances driven by beam-induced multipacting?
    Compare with simple resonance model developed in PAC03 paper.

(e) What is the effect of using different SEY models? Are the universal
    features that are **not** dependent on the details of the SEY model?
    What features need more attention (i.e. rediffused electrons and
    photon reflectivity)?

**B. Simulations for CesrTA**

It is proposed to reconfigure CESR into a test-bed for the ILC damping
ring. Electron cloud simulations were performed for CesrTA, to compare
with experiments reported by Mark Palmer at ECLOUD07. In these
experiments, the bunch-by-bunch tune shift is measured in a bunch train
and a witness bunch some distance after the train. The tune shift is
believed to be attributed to the electron cloud.

> \(1\) Unlike the APS case, the simulation technique of 'culling' (not
> present in the earlier version of POSINST) is important for CesrTA.
> Without culling, primary electron production soon stops, leading to
> incorrect build-up of the electron cloud. Primary photoelectrons are
> potentially more important in CESR because there is no antechamber.
>
> \(2\) There are large differences between the electron cloud in drifts
> and dipoles. In particular, in the case of drifts the cloud
> more-or-less uniformly fills the chamber. In dipoles, one can clearly
> see 'stripes', which are also seen in experiments elsewhere (e.g.,
> CERN).
>
> \(3\) The cloud build-up is also different in drifts and dipoles. In
> the former the build-up is rapid, close to exponential, and it
> saturates. In dipoles the build-up is more linear.
>
> \(4\) The overall shape of the build-up in the dipole simulations
> agrees well with experiments. This is encouraging, since the dipoles
> cover a large fraction of the CESR ring (63% in CESR vs. 22% in APS).
>
> \(5\) However, the decay of the cloud, after passage of all the
> bunches, is much faster than in the experiment. This is true for both
> the drift and the dipoles.

The following issues need to be pursued:

> \(a\) Can the agreement in the cloud build-up be made quantitative?
>
> \(b\) What determines the decay? Is electron cloud trapping in the
> quadrupoles responsible, as postulated elsewhere (e.g., PSR, KEKB).
> The latter would require modeling studies using WARP.
>
> \(c\) Data exists for positrons as well as electrons, which show
> asymmetries. Can this be reproduced, even qualitatively, by the
> simulations?
>
> \(d\) Can the simulations be used to make predictions and suggestions
> for experiments that may help to better understand electron cloud
> effects in CesrTA? In particular, can they explain the differences in
> the single-bunch effect between CESR and KEKB?

**C. Code development -- Culling**

A major problem with electron cloud simulations is that, due to the high
secondary electron emission, very soon the number of macroparticles in
the simulations becomes unmanageable. Some codes, such as HEADTAIL,
solve this problem by producing only one secondary electron (of varying
charge) per collision, but this is unphysical. POSINST deals with this
problem by 'culling' particles, i.e. thinning out the particle
distribution, every time the number of macroparticles exceeds a maximum.
This is statistically valid, as long as the culling procedure does not
change the statistical properties of the distribution (for example the
first few moments). After culling the charges of the remaining
macroparticles are renormalized to conserve charge.

However, in the present culling algorithm, particles with the heaviest
charge are eliminated. There is no guarantee that these particles are
uniformly distributed in phase-space. Therefore, such a culling
algorithm could change the cloud distribution, and therefore affect the
further build-up of the cloud.

A more reasonable way of doing the culling would be to do a fine-grained
culling in phase-space, so that the size of the distribution is reduced
without affecting its shape. To implement this, one would have to bin
all the particles in 6-dimensional phase-space, and then do the culling
in each bin -- for example, eliminate half the particles in each bin.
This method would certainly keep the distribution unperturbed, but has
the disadvantage that it is computationally expensive, since binning has
to be done in 6 dimensions. This disadvantage is mitigated by the fact
that the algorithm is intrinsically parallelizable.

Now, the space-charge force cares only for the spatial distribution of
the particles. Therefore, as a first step, it is useful to do the
culling just in the 3 spatial dimensions, and assess its impact. A
culling algorithm to do this was written and tested with a Gaussian
beam. We are now in the midst of integrating the algorithm into POSINST.

**D. Future work**

Some possible directions for future work:

> \(1\) Detailed simulations of CesrTA, designed to drive further
> experiments. Study electron cloud lifetime. Continue comparisons with
> RFA data after they are installed. Refine primary and secondary
> emission parameters. Contribute to design of CesrTA and electron cloud
> diagnostics in wigglers.
>
> \(2\) Detailed simulations of the ILC Damping ring, using a real
> lattice, and with beam dynamics (i.e. using WARP).
>
> \(3\) Detailed POSINST simulations of the APS buildup experiments.
> Model the instability using a beam dynamics code (such as WARP).
>
> \(4\) A major problem with predicting the electron cloud effect is
> that many of the results seem to depend very strongly on the details
> of the SEY -- which is poorly measured and understood. It would be
> useful to employ simulations to explore if there are universal
> features that are **not** strongly dependent on the SEY. And if so,
> how relevant are they for real accelerator parameters? What parameters
> need more attention (e.g. rediffused electrons, photon reflectivity,
> and photoemission model)?
>
> \(5\) Study 3D modeling of electron cloud trapping in quadrupoles and
> compare short bunches with long bunches: are there different regimes?
>
> \(6\) Almost all electron cloud studies (simulation or experiment)
> focus on one kind of element -- drift, or dipole, or quadrupole, etc.
> In the real ring, the beam passes through all these elements. It would
> therefore be useful to start with a simple model of a storage ring
> with drifts, dipole and quadrupoles, and study cloud evolution and
> beam dynamics in the ring as a whole. Study convergence; i.e., what
> kind and how many cloud elements are required. This should give
> insight into the importance of studying the electron cloud effect in
> such a holistic manner. If it turns out that this is important, one
> could then extend the study to a real lattice, such as for the ILC DR.
>
> \(7\) Code development. The electron cloud build-up could be
> integrated into ELEGANT, so that one can study build-up in the real
> lattice. The cloud algorithms could also be improved and made fully
> self-consistent.