I will present an update on the ECLOUD calculations at tomorrow's
RFA meeting. A lot has been done lately, so in the interest of
time, I will limit the presentation to three subtopics:
1) azimuthal distribution of p.e. hitting the beampipe wall
and the REFL parameter
2) systematics of electric field gradient calculations
3) accelerations of the cloud macroparticles by the beam bunch
passage and by the cloud space charge, and the effects on
the distribution of kinetic energies in the cloud
In the context of these results, I will seek your input on prioritizing
the outstanding issues.
1) I have added some plots to the standard set of the
cloud-characterizing analysis by extracting the positions and
velocities of all particles hitting the wall, which at present is
modelled as an ellipse with half-axes of of 4.5 cm and 2.5 cm.
For example, here is a 2D plot of the positions for a baseline set of
parameters which has the fraction of primary p.e. produced by
far-upstream-multiply-reflected sr photons (uniformly distributed in
azimuth) REFL=20%:
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/wall_219_3.jpg
The horizontal, vertical and longitudinal position distributions
are here:
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/wall_219_1.jpg
Here is how it changes if REFL is set to 100%:
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/wall_224_3.jpg
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/wall_224_1.jpg
Now an equal number of particles hit the left and right sides of the wall.
Offhand I do not know why so fewer macroparticles hit the wall with
this value of REFL.
As an aside, I mention that there is a substantial effect on the
field gradients: dEy/y is similar, but dEx/x is much larger for the
100% REFL. This means that our tune measurements
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/e+qxqy.jpg
favor the lower value for REFL.
2) Systematics of the electric field calculation: the preceding remark
concerning the field gradients is supported by these plots:
REFL=20%
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/ecloud_219_13.jpg
REFL=100%
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/ecloud_224_13.jpg
While it is encouraging that we obtain the expected vertical field
gradient of 3000 V/m^2 corresponding to a tune shift of about
850 khz, there is clearly some source of instability in the
calculation. The field calculation is made faster by summing over
charges on a 21x21 grid rather than summing over the actual
macroparticle positions. This is causing instability at the level
we see, since going to a 51x51 grid changes the gradients by similar
amounts. This makes the ecloud calculation much too slow however.
These plots show the field values evaluated after the 15th bunch passage,
i.e. at T = 15 * 14 = 210 ns. The first 10 bunches are filled, the next 5 empty.
21x21
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/qgrid_219_3.jpg
51x51
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/qgrid_225_3.jpg
Also, the ECLOUD field calculation requires an elliptical beampipe,
and we know the calculated gradients depend strongly on the beampipe
shape. I have some suggestions for improving the calculation which
we can discuss.
3) Magnitudes of cloud space charge and beam kicks: effects on the
energy spectrum hitting the wall. Some examples of trajectories
and kicks can be instructive.
Trajectories:
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/traj_219.jpg
Momenta and energy:
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/mom_219.jpg
Kicks:
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/ecloud_219_7.jpg
Energy Distribution:
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/ecloud_219_9.jpg
If we increase the current in the 10 bunches from 0.75 mA to 7.5 mA,
the beam kicks get very large and the energy distribution above
100 eV becomes much more populated:
Trajectories:
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/traj_221.jpg
Momenta and energy:
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/mom_221.jpg
Kicks:
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/ecloud_221_7.jpg
Energy Distribution:
http://www.lepp.cornell.edu/~critten/cesrta/ecloud/6may08/ecloud_221_9.jpg
See you tomorrow, Jim
========================================================
James Crittenden Tel. (607) 255-9424
Wilson Synchrotron Laboratory Fax (607) 255-8062
Cornell University
Ithaca, New York 14853-8001
========================================================
