Subject: Field Gradients in ECLOUD From: Jim Crittenden Date: Fri, 28 Mar 2008 13:41:03 -0400 To: David Rubin , Mark Palmer Hi Dave, Mark I have some results of a study into the effect of the fraction of reflected p.e.-producing photons (REFL) on the electric field gradients at the beam resulting from the electron cloud. The standard set of plots from these calculations now includes a plot of the azimuthal distribution of the rate of electrons hitting the beampipe wall at the time the abort gap begins, as well as of the power per m2 on the wall. The latter is just the former weighted by the energy of the electrons hitting the wall. In the plot I call it an 'energy flux.' In order to compare to the tune shift plots on page 9 of MAP's March 5, 2008 TILC08 talk, I used a bunch pattern of 10 0.75 mA bunches prior to the 5-bunch abort gap. Since there are no empty bunches following the filled bunches, there is no information on how the gradients decay following the passage of the last filled bunch, since they are calculated only at the moment a bunch arrives. Earlier calculations including empty bunches have shown that the rate of decrease of the gradients depends strongly on REFL and on the presence of a magnetic field. DLR has calculated that a field gradient of 1000 V/m2 gives a tune shift of 280 Hz. According to the TILC08 talk we are looking for a vertical gradient after ten bunches of about 850 Hz, i.e. 3000 V/m2, and a horizontal gradient of about 60 Hz, i.e. 200 Hz. Let's first look at the effect of REFL on the azimuthal distributions. Here is the example of the cloud in a b-field-free region after ten bunch passages: REFL = 0% http://www.lepp.cornell.edu/~critten/cesrta/notes/28mar08/ecloud_194_5.pdf REFL = 40% http://www.lepp.cornell.edu/~critten/cesrta/notes/28mar08/ecloud_197_5.pdf Higher REFL results in a more uniform azimuthal distribution, as expected. Prior calculations with EFL=100% showed a nearly uniform azimuthal distribution. I don't consider high REFL values here because they give dramatically wrong values for the ratio of vertical to horizontal field gradients. A magnetic field has a big effect on these azimuthal distributions. Here is the effect of an 800 G vertical dipole field on the REFL=40% case: http://www.lepp.cornell.edu/~critten/cesrta/notes/28mar08/ecloud_193_5.pdf The field concentrates the rate and energy flux at zero azimuth. Notice also that there is are enhancements on the upper and lower walls which weren't there without the B field. Now let's turn to the field gradients at the beam. Here they are for the first two cases above. REFL = 0% http://www.lepp.cornell.edu/~critten/cesrta/notes/28mar08/ecloud_194_8.pdf REFL = 40% http://www.lepp.cornell.edu/~critten/cesrta/notes/28mar08/ecloud_197_8.pdf It's nice to see that we get the expected vertical gradient magnitude of about 3000 V/m2. The horizontal gradient is somewhat too large, but for these smaller values (400-1200 V/m2) the calculation is somewhat unstable (as are the measurements.) There appears to be a slight preference for REFL=40%, but the horizontal gradient in neither case is down by a factor of 17 as the measurements indicate. Here are the results for the gradients in tabular form for the calculations I have done so far. The complete sets of plots are available as multipage pdf's in this same web directory: http://www.lepp.cornell.edu/~critten/cesrta/notes/28mar08/ B=0 | B=800 G --- | ------- REFL 0 10 20 40 | 0 10 20 40 ------ ------ ------ ------ | ------ ------ ------ ------ | Job nr 194 195 198 197 | 190 191 192 193 | dEy/dy 3200 3000 3200 3500 | 65 200 600 1100 | dEx/dx 800 500 400 400 | -75 100 300 800 Clearly we have more work to do before we get good agreement with the tune shift measurements. All suggestions welcome. Frank Z has suggested that his code HEADTAIL, which uses ECLOUD output files, may have a more accurate calculation of the field at the beam. Other options are to check the gradient time rates of decrease following passage of the last bunch, which we can compare to the witness bunch tune-shift measurements, and to compare the results for an electron beam to the measurements shown on page 11 of the TILC08 talk. -- Jim ======================================================== James Crittenden Tel. (607) 255-9424 Wilson Synchrotron Laboratory Fax (607) 255-8062 Cornell University Ithaca, New York 14853-8001 ========================================================