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<div id="content">
<h1 class="title">ARC1</h1>
<div id="outline-container-1" class="outline-2">
<h2 id="sec-1"><span class="section-number-2">1</span> Requirements </h2>
<div class="outline-text-2" id="text-1">
<ul>
<li>
The TWISS values for the ARC1 section must be independent of how
they are generated. That is, stand alone ARC1 must return the same
TWISS values as LINAC1+ARC1 combined.
<p>
– This means that the input TWISS values must be exactly
identical to the output of LINAC1.
</p>
<p>
– This also assumes that the input TWISS values to LINAC1 are
correct.
</p>
</li>
<li>
The TWISS values in ARC1 are symmetric about MQA1A21
</li>
<li>
Between the Arc bending magnets the Quadrupoles K1 and distances
are symmetric about MQA1A21
</li>
<li>
The ARC proper entrance/exit β values are equal
</li>
<li>
The ARC proper entrance/exit α values are equal and opposite
</li>
<li>
The TWISS values at the end of the Recombiner are matched exactly
to the LINAC2 entrance TWISS.
<p>
– Note, this can be achieved by also modifying the LINAC2
entrance TWISS values to be exactly those of the ARC1 exit
values.
</p>
<p>
– Or some combination of the two, fit to match, but transfer the
exact final ARC1 values as the LINAC2 entrance values.
</p></li>
</ul>
</div>
</div>
<div id="outline-container-2" class="outline-2">
<h2 id="sec-2"><span class="section-number-2">2</span> TWISS parameters in original Optim/Elegant files for Arc1 </h2>
<div class="outline-text-2" id="text-2">
</div>
<div id="outline-container-2.1" class="outline-3">
<h3 id="sec-2.1"><span class="section-number-3">2.1</span> β<sub>x</sub> </h3>
<div class="outline-text-3" id="text-2.1">
<p><img src="./ARC1originalBETAX.jpg" alt="./ARC1originalBETAX.jpg" />
</p></div>
</div>
<div id="outline-container-2.2" class="outline-3">
<h3 id="sec-2.2"><span class="section-number-3">2.2</span> β<sub>y</sub> </h3>
<div class="outline-text-3" id="text-2.2">
<p><a href="#sec-2.2"><img src="ARC1_original_betay.jpg"/></a>
</p></div>
</div>
<div id="outline-container-2.3" class="outline-3">
<h3 id="sec-2.3"><span class="section-number-3">2.3</span> η<sub>x</sub> </h3>
<div class="outline-text-3" id="text-2.3">
<p><a href="#sec-2.3"><img src="ARC1_original_etax.jpg"/></a>
</p></div>
</div>
<div id="outline-container-2.4" class="outline-3">
<h3 id="sec-2.4"><span class="section-number-3">2.4</span> η<sub>y</sub> </h3>
<div class="outline-text-3" id="text-2.4">
<p><a href="#sec-2.4"><img src="ARC1_original_etay.jpg"/></a>
</p></div>
</div>
</div>
<div id="outline-container-3" class="outline-2">
<h2 id="sec-3"><span class="section-number-2">3</span> <span class="todo TODO"> TODO</span> [11/15] Steps towards self-consistency </h2>
<div class="outline-text-2" id="text-3">
</div>
<div id="outline-container-3.1" class="outline-3">
<h3 id="sec-3.1"><span class="section-number-3">3.1</span> <span class="done DONE"> DONE</span> Retrieve NL input parameters from Optim deck </h3>
<div class="outline-text-3" id="text-3.1">
<p><span class="timestamp-wrapper"> <span class="timestamp">2010-03-02 Tue 12:09</span></span><br/>
</p><ul>
<li id="sec-3.1.1">Art++ Inj and North linac Optim deck at start of D39 <br/>
<ul>
<li>
β<sub>x</sub> = 28.9072 m
</li>
<li>
α<sub>x</sub> = -2.45782
</li>
<li>
β<sub>y</sub> = 6.18386 m
</li>
<li>
α<sub>y</sub> = 1.30688
</li>
<li>
η<sub>x</sub> = 0.00189354 This should be zero
</li>
<li>
η<sub>y</sub> = 0
</li>
<li>
η<sub>x</sub><sup>′</sup> = 0.000149481 This should be zero
</li>
<li>
η<sub>y</sub><sup>′</sup> = 0
</li>
</ul>
</li>
<li id="sec-3.1.2">Present values in LINAC1.ele <br/>
<ul>
<li>
β<sub>x</sub>=2.863532e+01
</li>
<li>
α<sub>x</sub>=-2.4307
</li>
<li>
β<sub>y</sub>=6.178298e+00
</li>
<li>
α<sub>y</sub>=1.3037
</li>
<li>
Z = -154.68952
</li>
</ul>
</li>
<li id="sec-3.1.3">AB North linac Optim deck starts at beginning (D1000) <br/>
<ul>
<li>
β<sub>x</sub> = 37.5812 m
</li>
<li>
α<sub>x</sub> = -2.80987
</li>
<li>
β<sub>y</sub> = 3.15303 m
</li>
<li>
α<sub>y</sub> = 0.6171
</li>
<li>
η<sub>x</sub> = η<sub>y</sub> = η<sub>x</sub><sup>′</sup> = η<sub>y</sub><sup>′</sup> = 0
</li>
<li>
s = -0.90004 m
</li>
<li>
Z = -153.11452
</li>
</ul>
</li>
<li id="sec-3.1.4">Notes <br/>
The difference in Z is 1.575 m between AB Optim and the
elegant/Art++ decks, which is the exact length of an
added drift in LINAC1.lte (D1000A). This D1000A (elegant)
corresponds to D39 (optim). So one must pick TWISS parameters at front
of D39, cannot use AB's deck.
<p>
The difference between the Art++ and the elegant decks is small,
but enough to cause grief.
</p>
</li>
</ul>
</div>
</div>
<div id="outline-container-3.2" class="outline-3">
<h3 id="sec-3.2"><span class="section-number-3">3.2</span> <span class="done DONE"> DONE</span> Modify LINAC1.ele to include the correct input parameters </h3>
<div class="outline-text-3" id="text-3.2">
<p>Use the Art++ D39 values:
</p>
<pre class="example">beta_x=2.89072e+01, alpha_x=-2.45782,
beta_y=6.18386e+00, alpha_y=1.30688,
</pre>
</div>
</div>
<div id="outline-container-3.3" class="outline-3">
<h3 id="sec-3.3"><span class="section-number-3">3.3</span> <span class="done DONE"> DONE</span> Run LINAC1.ele and extract final TWISS values </h3>
<div class="outline-text-3" id="text-3.3">
<p><span class="timestamp-wrapper"> <span class="timestamp">2010-03-02 Tue</span></span><br/>
</p><ul>
<li>
β<sub>x</sub> = 6.062352e+00
</li>
<li>
α<sub>x</sub> = -2.087257e-02
</li>
<li>
β<sub>y</sub> = 2.723758e+01
</li>
<li>
α<sub>y</sub> = -1.853349e+00
</li>
<li>
η<sub>xy</sub> = η<sub>xy</sub><sup>′</sup> = 0
</li>
<li id="sec-3.3.1">Notes <br/>
These are slightly different than the values in ARC1.ele
(revision1.7). TWISS values found for ARC1 entrance.
<pre class="example">beta_x=6.35476, alpha_x=-0.0575519,
beta_y=27.1339, alpha_y=-1.86361
</pre>
</li>
</ul>
</div>
</div>
<div id="outline-container-3.4" class="outline-3">
<h3 id="sec-3.4"><span class="section-number-3">3.4</span> <span class="done DONE"> DONE</span> Modify ARC1.ele to use the LINAC1.ele exit TWISS as input </h3>
<div class="outline-text-3" id="text-3.4">
<p>Modified ARC1.ele to reflect the output of LINAC1, twiss<sub>output</sub>
parameters:
</p>
<pre class="example">beta_x=6.06352, alpha_x=-2.087257e-2,
beta_y=27.23758, alpha_y=-1.853349
</pre>
</div>
</div>
<div id="outline-container-3.5" class="outline-3">
<h3 id="sec-3.5"><span class="section-number-3">3.5</span> <span class="done DONE"> DONE</span> Verify quadrupole symmetry in ARC1.lte </h3>
<div class="outline-text-3" id="text-3.5">
<p><span class="timestamp-wrapper"> <span class="timestamp">2010-03-09 Tue 13:03</span></span><br/>
The quadrupole magnets between the first and last dipole bends
should be symmetric (in focal length and location) about the center
(MQA1A21) of the Arc. The tables below show that the locations are
symmetric at the tens of micron level and the focal lengths (K1s)
are spot on.
</p>
<ul>
<li id="sec-3.5.1">Arc1 Quad magnet S coordinate symmetry check <br/>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption></caption>
<colgroup><col align="left" /><col align="left" /><col align="right" /><col align="right" /><col align="right" />
</colgroup>
<thead>
<tr><th scope="col">First Half</th><th scope="col">Second Half</th><th scope="col">Distance from center(first half)</th><th scope="col">Distance from center(2nd half)</th><th scope="col">Δ(first-second)</th></tr>
</thead>
<tbody>
<tr><td>MQB1A03</td><td>MQB1A39</td><td>114.52362</td><td>114.52363</td><td>-9.99999970474619e-06</td></tr>
<tr><td>MQB1A04</td><td>MQB1A38</td><td>110.86681</td><td>110.86681</td><td>3.41060513164848e-13</td></tr>
<tr><td>MQB1A05</td><td>MQB1A37</td><td>107.21</td><td>107.20999</td><td>1.00000003158129e-05</td></tr>
<tr><td>MQB1A06</td><td>MQB1A36</td><td>95.0286899999999</td><td>95.0286899999997</td><td>2.27373675443232e-13</td></tr>
<tr><td>MQB1A07</td><td>MQB1A35</td><td>82.8473899999999</td><td>82.8473799999997</td><td>1.00000002305478e-05</td></tr>
<tr><td>MQB1A08</td><td>MQB1A34</td><td>79.1905699999999</td><td>79.1905699999997</td><td>2.55795384873636e-13</td></tr>
<tr><td>MQB1A09</td><td>MQB1A33</td><td>75.53375</td><td>75.5337599999998</td><td>-9.99999977580046e-06</td></tr>
<tr><td>MQB1A11</td><td>MQB1A31</td><td>63.3524599999999</td><td>63.3524599999999</td><td>5.6843418860808e-14</td></tr>
<tr><td>MQB1A13</td><td>MQB1A29</td><td>51.1711599999999</td><td>51.1711699999999</td><td>-9.99999997475243e-06</td></tr>
<tr><td>MQB1A14</td><td>MQB1A28</td><td>47.5143499999999</td><td>47.51435</td><td>-8.5265128291212e-14</td></tr>
<tr><td>MQB1A15</td><td>MQB1A27</td><td>43.85754</td><td>43.85753</td><td>1.00000000315958e-05</td></tr>
<tr><td>MQB1A16</td><td>MQB1A26</td><td>31.6762299999999</td><td>31.67623</td><td>-8.5265128291212e-14</td></tr>
<tr><td>MQB1A17</td><td>MQB1A25</td><td>19.4949299999999</td><td>19.49492</td><td>9.9999998894873e-06</td></tr>
<tr><td>MQB1A18</td><td>MQB1A24</td><td>15.83811</td><td>15.83811</td><td>0</td></tr>
<tr><td>MQB1A19</td><td>MQB1A23</td><td>12.18129</td><td>12.1813000000001</td><td>-1.00000000600176e-05</td></tr>
</tbody>
<tbody>
<tr><td></td><td></td><td></td><td>Total</td><td>1.66e-12</td></tr>
</tbody>
</table>
</li>
<li id="sec-3.5.2">Arc1 Quad focal length check <br/>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption></caption>
<colgroup><col align="left" /><col align="left" /><col align="right" /><col align="right" /><col align="right" />
</colgroup>
<thead>
<tr><th scope="col">First Half</th><th scope="col">Second Half</th><th scope="col">K1 (first half)</th><th scope="col">K1 (2nd half)</th><th scope="col">Δ</th></tr>
</thead>
<tbody>
<tr><td>MQB1A03</td><td>MQB1A39</td><td>-1.16578</td><td>-1.16578</td><td>0</td></tr>
<tr><td>MQB1A04</td><td>MQB1A38</td><td>2.13112</td><td>2.13112</td><td>0</td></tr>
<tr><td>MQB1A05</td><td>MQB1A37</td><td>-0.84544</td><td>-0.84544</td><td>0</td></tr>
<tr><td>MQB1A06</td><td>MQB1A36</td><td>0.79145</td><td>0.79145</td><td>0</td></tr>
<tr><td>MQB1A07</td><td>MQB1A35</td><td>-0.849229</td><td>-0.849229</td><td>0</td></tr>
<tr><td>MQB1A08</td><td>MQB1A34</td><td>1.56739</td><td>1.56739</td><td>0</td></tr>
<tr><td>MQB1A09</td><td>MQB1A33</td><td>-0.757331</td><td>-0.757331</td><td>0</td></tr>
<tr><td>MQB1A11</td><td>MQB1A31</td><td>1.235450559220401</td><td>1.235450559220401</td><td>0</td></tr>
<tr><td>MQB1A13</td><td>MQB1A29</td><td>-0.897281</td><td>-0.897281</td><td>0</td></tr>
<tr><td>MQB1A14</td><td>MQB1A28</td><td>1.39555</td><td>1.39555</td><td>0</td></tr>
<tr><td>MQB1A15</td><td>MQB1A27</td><td>-0.854162</td><td>-0.854162</td><td>0</td></tr>
<tr><td>MQB1A16</td><td>MQB1A26</td><td>0.539361</td><td>0.539361</td><td>0</td></tr>
<tr><td>MQB1A17</td><td>MQB1A25</td><td>-1.00616</td><td>-1.00616</td><td>0</td></tr>
<tr><td>MQB1A18</td><td>MQB1A24</td><td>1.29706</td><td>1.29706</td><td>0</td></tr>
<tr><td>MQB1A19</td><td>MQB1A23</td><td>-0.5900030000000001</td><td>-0.5900030000000001</td><td>0</td></tr>
</tbody>
</table>
</li>
</ul>
</div>
</div>
<div id="outline-container-3.6" class="outline-3">
<h3 id="sec-3.6"><span class="section-number-3">3.6</span> <span class="done DONE"> DONE</span> Match to η<sub>y</sub>=η<sub>y</sub><sup>′</sup>=0 at the 1SD and 1RD match points </h3>
<div class="outline-text-3" id="text-3.6">
<p><span class="timestamp-wrapper"> <span class="timestamp">2010-03-02 Tue 19:50</span></span><br/>
</p><ul>
<li id="sec-3.6.1">1S η location (MKMATCH1SD) <br/>
<ul>
<li>
MQB1S02.K1 = 1.97364878
</li>
<li>
MQB1S03.K1 = -2.6228056
</li>
<li>
η<sub>y</sub> = -2.5e-11 m
</li>
<li>
η<sub>yp</sub> = 1.2e-12
</li>
</ul>
</li>
<li id="sec-3.6.2">1R η location (end of recombiner) <br/>
<ul>
<li>
magnet:K1 Δ
</li>
<li>
MQB1R09.K1: 1.794174816572240e+00 2.784816572239723e-03
</li>
<li>
MQB1R10.K1: -1.224998094708481e+00 1.905291519221919e-06
</li>
<li>
η<sub>y</sub> = 9.931705e-11
</li>
<li>
η<sub>yp</sub> = -3.497203e-15
</li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-3.7" class="outline-3">
<h3 id="sec-3.7"><span class="section-number-3">3.7</span> <span class="done DONE"> DONE</span> Modify Lattice: set matched quad values </h3>
<div class="outline-text-3" id="text-3.7">
</div>
</div>
<div id="outline-container-3.8" class="outline-3">
<h3 id="sec-3.8"><span class="section-number-3">3.8</span> <span class="done CANCELED"> CANCELED</span> Measure M<sub>56</sub> across the Spreader, Arc, and Recombiner </h3>
<div class="outline-text-3" id="text-3.8">
<p><span class="timestamp-wrapper"> <span class="timestamp">2010-03-03 Wed 11:18</span></span><br/>
Is this really a necessary step? Why not simply require M<sub>56</sub>(End
of 1R) = 0, by adjusting quads in the Arc? No need to measure
anything, just null it out.
</p></div>
</div>
<div id="outline-container-3.9" class="outline-3">
<h3 id="sec-3.9"><span class="section-number-3">3.9</span> <span class="done DONE"> DONE</span> Optimize <del>1A16</del> 1A11 and 1A31 to achieve M<sub>56</sub> = 0 </h3>
<div class="outline-text-3" id="text-3.9">
<p>M<sub>56</sub>(Arc) = -(M<sub>56</sub>(Spreader) + M<sub>56</sub>(Recombiner))
<span class="timestamp-wrapper"> <span class="timestamp">2010-03-03 Wed 07:30</span></span><br/>
Are these the right quads? Adjusting these quads will break the
symmetry of quad settings across the arc. Would MQB1A11 and
MQB1A31 be a better match?
</p>
<p>
<span class="timestamp-wrapper"> <span class="timestamp">2010-03-03 Wed 11:24</span></span><br/>
1A11 and 1A31 is the correct pair, where did 1A16 come from?
</p>
<ul>
<li id="sec-3.9.1">Results <br/>
<pre class="example">Optimization results:
optimization function has value 1.09266626400112e-23
Terms of equation:
MKMATCH1R#1.R56 0 - sqr: 1.092666264001120e-23
A total of 88 function evaluations were made.
Optimum values of variables and changes from initial values:
MQB1A11.K1: 1.237074954941993e+00 1.624395721592231e-03
MQB1A31.K1: 1.237074954941993e+00
</pre>
<p>
M<sub>56</sub> for the entire spreader-arc-recombiner lattice after this
fit is:
</p>
<pre class="example">M_{56}(end of 1R) = -3.305550e-12 m
</pre>
</li>
</ul>
</div>
</div>
<div id="outline-container-3.10" class="outline-3">
<h3 id="sec-3.10"><span class="section-number-3">3.10</span> <span class="done DONE"> DONE</span> Modify Lattice with matched quad values </h3>
<div class="outline-text-3" id="text-3.10">
</div>
</div>
<div id="outline-container-3.11" class="outline-3">
<h3 id="sec-3.11"><span class="section-number-3">3.11</span> <span class="todo INPROGRESS"> INPROGRESS</span> Optimize Spread matching quads for symmetry </h3>
<div class="outline-text-3" id="text-3.11">
<p>Use the spreader matching quads to achieve the desired symmetry:
β<sub>entrance</sub> = β<sub>exit</sub>
and α<sub>entrance</sub> = -α<sub>exit</sub>
</p>
<p>
<span class="timestamp-wrapper"> <span class="timestamp">2010-03-03 Wed 11:16</span></span><br/>
In discussion with Alex, it might be useful to split 1A21 quad in
half and require that: α<sub>xy</sub> = η<sub>xy</sub><sup>′</sup> =0 at the
midplane of the ARC. This adds four more constraints and might
make convergence faster.
</p>
<p>
<span class="timestamp-wrapper"> <span class="timestamp">2010-03-04 Thu 14:30</span></span><br/>
These extra constraints did really provide any benefit
</p>
<ul>
<li id="sec-3.11.1">Need to restrict β<sub>xy</sub> <br/>
<span class="timestamp-wrapper"> <span class="timestamp">2010-03-05 Fri 14:30</span></span><br/>
The fit is converging to solution with very large β<sub>x</sub>. In
order to get control the twiss<sub>analysis</sub> command is used and a
constraint on the maximum β<sub>x</sub> and β<sub>y</sub> across Arc proper is
invoked.
<p>
twiss<sub>analysis</sub>:
</p>
<pre class="example">&twiss_analysis
start_name = "MKMATCH1S"
end_name="MKMATCH1A"
tag="ARC1"
&end
</pre>
<p>
constraint:
</p>
<pre class="example">&optimization_term
term="ARC1.max.betax 100 0.1 segt"
&end
&optimization_term
term="ARC1.max.betay 100 0.1 segt"
&end
</pre>
</li>
</ul>
</div>
</div>
<div id="outline-container-3.12" class="outline-3">
<h3 id="sec-3.12"><span class="section-number-3">3.12</span> <span class="done DONE"> DONE</span> Modify Lattice with matched quad values </h3>
<div class="outline-text-3" id="text-3.12">
<p>
Optimum values of variables and changes from initial values:
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption></caption>
<colgroup><col align="left" /><col align="right" /><col align="right" /><col align="right" />
</colgroup>
<thead>
<tr><th scope="col">Quad</th><th scope="col">Original K1</th><th scope="col">New K1 value</th><th scope="col">Δ from initial</th></tr>
</thead>
<tbody>
<tr><td>MQB1S04.K1:</td><td>-2.30542</td><td>-2.308093368585293e+00</td><td>0.0027</td></tr>
<tr><td>MQB1S05.K1:</td><td>2.31853</td><td>2.275024120883677e+00</td><td>0.0435</td></tr>
<tr><td>MQB1S06.K1:</td><td>0.0746592</td><td>7.818336278920536e-02</td><td>-0.0035</td></tr>
<tr><td>MQB1S07.K1:</td><td>-1.87678</td><td>-1.878658827305099e+00</td><td>0.0019</td></tr>
<tr><td>MQB1S08.K1:</td><td>1.52092</td><td>1.669917945157796e+00</td><td>-0.1490</td></tr>
<tr><td>MQB1S09.K1:</td><td>-1.50962</td><td>-1.500127277897621e+00</td><td>-0.0095</td></tr>
<tr><td>MQB1S10.K1:</td><td>0.74106</td><td>7.585530020790612e-01</td><td>-0.0175</td></tr>
<tr><td>MQB1E01.K1</td><td>-0.373191</td><td>-3.641376337719247e-01</td><td>-0.0091</td></tr>
<tr><td>MQB1E02.K1:</td><td>0.556494</td><td>5.557303950127344e-01</td><td>0.0008</td></tr>
<tr><td>MQB1E03.K1:</td><td>-0.613057</td><td>-6.105642051223680e-01</td><td>-0.0025</td></tr>
<tr><td>MQB1A01.K1:</td><td>1.05041</td><td>1.051848906785837e+00</td><td>-0.0014</td></tr>
</tbody>
</table>
<span class="timestamp-wrapper"> <span class="timestamp">2010-03-09 Tue 13:16</span></span><br/>
The above table results in an improved Arc1 TWISS symmetry but it
is still not symmetric. The above values were obtained with a fit
that did not allow the β<sub>xy</sub> go above 75m in the Arc. Better
symmetries are obtained with large β values. Try again!
<span class="timestamp-wrapper"> <span class="timestamp">2010-03-09 Tue 17:08</span></span><br/>
Added the 1E quads into the fit. They were not moved much by the
optimization. Need to add plots. β<sub>x</sub> is visually more
symmetric than the initial.
</div>
</div>
<div id="outline-container-3.13" class="outline-3">
<h3 id="sec-3.13"><span class="section-number-3">3.13</span> <span class="todo WAITING"> WAITING</span> Re-run ARC1 elegant deck for verification </h3>
<div class="outline-text-3" id="text-3.13">
<ul>
<li>
Verify that η=η<sup>′</sup> = 0 at the 1SD and 1RD match points
</li>
<li>
Verify that the TWISS parameters are symmetric
</li>
</ul>
<p><span class="timestamp-wrapper"> <span class="timestamp">2010-03-09 Tue 13:15</span></span><br/>
The ARC1.lte deck as saved still has a visible asymmetry. Trying
improve the fit.
</p>
</div>
</div>
<div id="outline-container-3.14" class="outline-3">
<h3 id="sec-3.14"><span class="section-number-3">3.14</span> <span class="todo TODO"> TODO</span> Add LINAC1+ARC1 together </h3>
<div class="outline-text-3" id="text-3.14">
</div>
</div>
<div id="outline-container-3.15" class="outline-3">
<h3 id="sec-3.15"><span class="section-number-3">3.15</span> <span class="todo TODO"> TODO</span> Run LINAC1<sub>ARC1</sub> and compare TWISS with stand alone ARC1 </h3>
<div class="outline-text-3" id="text-3.15">
</div>
</div>
</div>
<div id="postamble">
<p class="author"> Author: Arne Freyberger
<a href="mailto:freyberg@localhost.localdomain"><freyberg@localhost.localdomain></a>
</p>
<p class="date"> Date: 2010-11-17 11:24:15 EST</p>
<p class="creator">HTML generated by org-mode 6.33x in emacs 23</p>
</div>
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