D. Rubin, S.Isaacman, A.Long
<br>March 17, 2005. (updated March 22, 2005)
<p>
<h1>Lattice with distributed radiation</h1>
<p>
<h3>Introduction</h3>
In order to understand the effect of the localized radiation source
of the wigglers, we consider alternative optics that have no wigglers at all.
In the model, all of the arc bending magnets are replaced with five
bends, each with 1/5 of the bending radius. There is negligible effect
on the machine geometry. Having increased the field of the dipoles by
a factor of 5, the radiation damping time is reduced to 20ms, essentially
the same as in the 12 wiggler cesr-c optics. The simulated specific luminosity
is nearly twice that in 12 wiggler cesr-c conditions. 
<p>
<h3> Model</h3>
The lattice is <a href="../cesrc/bmad_bend_5piece_v02.html">
bmad_bend_5piece_v02.lat </a>. The objective of the study was to explore the
effect of the wigglers as a localized radiation source. The configuration of
bends in the new lattice was chosen to reproduce the radiation damping time
of the 12 wiggler lattice. The same is not true for emittance, and energy spread.
The average energy radiated by an electron in a single turn is unchanged, but
the typical photon energy is much lower, and their number much higher. The energy
spread is less than half that of the standard cesr-c optics and the emittance
just over half. Otherwise, the distributed radiation lattice is typical of
cesr optics. It is compatible with nine trains of bunches. The interaction region
is the standard Phase III layout with compensation of the 1T CLEO solenoid with tilted
IR quads and IR skew quads. 

<h3> Simulation </h3>
The results of the simulation are shown below. The luminosity and
tuneshift parameter in the distributed bend lattice (bmad_bend_5piece_v02) are compared
with standard cesr-c (hibetainj_20040628_v01) and cesr-c with anti-solenoids (bmad_c_q0_040305).
The horizontal and vertical tunes for the standard cesr-c (Qx=0.532,Qy=0.594) 
and cesr-c with anti-solenoids (Qx=531, Qy=0.588) are
set based on tune scans. For the distributed bend lattice we used the anti-solenoid lattice tunes,
as a scan has not yet been computed. In all cases the synchrotron tune is -0.089.
Some of the distinguishing lattice parameters are summarized in the table
<p>
An unusual feature of the current dependence of the luminosity is the discontinuity
just above 1mA/bunch. There is some indication that this transition coincides
with an increase in bunch length. Possibly there is a corresponding increase 
in energy spread and the corresponding increase in vertical beam size
associated with the energy dependence of the solenoid compensation.
<p>




<table border=1>
<tr  valign=top ><td>
<tr><td>Lattice </td> <td> hibetainj_20040628_v01 </td>  <td> bmad_c_q0_040305 </td><td>bmad_bend_5piece_v02 </td></tr> 
<tr><td>Bunch length</td>   <td>1.32 cm </td>   <td> 1.32 cm </td> <td> 0.58 cm </td></tr> 
<tr><td>Energy spread </td> <td>8.4e-4  </td>   <td> 8.4e-4  </td> <td> 3.86e-4 </td></tr>
<tr><td>emittance     </td> <td>128 nm  </td>   <td>119 nm   </td> <td> 65 nm   </td></tr>
<tr><td>Damping time  </td> <td>50 ms   </td>   <td> 50ms    </td> <td> 43 ms   </td></tr> 
<tr><td>Lattice details </td><td><a href="../cesrc/hibetainj_20040628_v01.html">here</a></td>
                             <td><a href="../cesrc/bmad_c_q0_040305.html"> here</a> </td>
                             <td><a href="../cesrc/bmad_bend_5piece_v02.html"> here</a></td></tr>
</table>
<br>


<a href="../../~ajl59/log/16305-1_2.png"> Luminosity  </a> vs current is plotted for the
lattice with distributed radiation along with standard cesr-c optics (hibetainj) and
optics with compensating solenoids (bmad_c_q0_40305.lat, Q0 tilt=1.9deg). Tunes are Qx=0.531, Qy=0.588,
Qz=-0.089. 

The corresponding 
<a href="../beambeam/beambeam_tuneshift_030805-1_020305-1_160305-1_060305-1.gif"> beambeam tuneshift </a>
is shown for the same three as well as lattice c_020305, which is an example with compensating solenoids
but fixed Q0 tilt.
If we repeat the calculation at tunes that give best luminosity for the solenoid
off case, (see below), Qx=0.525, Qy=0.586 we get 
<a href="../beambeam/bb_062305_071205_060305-1.gif"> retuned luminosity </a> with 
<a href="../beambeam/bbts_062305_071205_060305-1.gif"> tuneshift </a>. Until we do a tune scan for the
1T optics, we cannot conclude for sure that the performance will compare as poorly as in the plot.
The same <a href="../beambeam/bb_062305_071205_071105.gif"> luminosity </a>
and <a href="../beambeam/bbts_062305_071205_071105.gif"> tuneshift </a> data is plotted along with standard cesr-c for reference

<tr><td><b>Lifetime/lost particles</b></td></tr>
<p>
Because we track relatively few particles (500) for only 100k turns (5 damping times), we have no
detailed lifetime information. The loss of even a single
particle corresponds to a lifetime of ~128 seconds and we are well below the
beambeam lifetime limiting current. The number of surviving particles is shown in the 
<a href="../../~ajl59/log/16305-1_3.png"> plot </a>
versus bunch current. There is a lost particle at a bunch current of 2.4mA in the distributed
bend optics, at 2.6mA in the lattice with anti-solenoid compensation. In the standard cesr-c optics
the threshold is 3.6mA (not shown). 
<tr><td><b>Solenoid off</b></td></tr>
<p>
A further idealization obtains if we consider a machine <a href="../cesrc/bmad_bend_5piece_nosol_v01.html">
bmad_bend_5piece_nosol_v01.lat </a> with distributed radiation and
no solenoid. With synchrotron tune set at -0.089, a <a href="../../~sni2/data/061405.gif"> tune scan </a>
indicates best luminosity at Qx=0.525, Qy=0.586 and we compute <a href="../cesrc/bb_062305.gif"> luminosity </a>
and <a href="../cesrc/bbts_062305.gif"> tune shift </a> vs current. Pretty nice.
<p>
<hr width=75%>
<p>