<HTML xmlns="http://www.w3.org/TR/REC-html40" xmlns:v = "urn:schemas-microsoft-com:vml" xmlns:o = "urn:schemas-microsoft-com:office:office" xmlns:w = "urn:schemas-microsoft-com:office:word" xmlns:m = "http://schemas.microsoft.com/office/2004/12/omml"><HEAD> <META content="text/html; charset=us-ascii" http-equiv=Content-Type> <META name=Generator content="Microsoft Word 14 (filtered medium)"> <STYLE></STYLE> </HEAD> <BODY dir=ltr lang=EN-US link=blue bgColor=white vLink=purple> <DIV dir=ltr> <DIV style="FONT-FAMILY: 'Arial'; COLOR: #000000; FONT-SIZE: 10pt"> <DIV>Rick,</DIV> <DIV> </DIV> <DIV>Thanks for this.</DIV> <DIV> </DIV> <DIV>It sounds to me like ECALC9 only includes a vector potential for DC magnets.</DIV> <DIV> </DIV> <DIV>For rf cavities, it sounds like neither the vector nor scalar potential are considered.</DIV> <DIV> </DIV> <DIV>This is inconsistent with the nominal rules of Hamiltonian dynamics.</DIV> <DIV> </DIV> <DIV>I am still trying to clarify whether we can get away with such apparent inconsistencies.</DIV> <DIV> </DIV> <DIV>--Kirk</DIV> <DIV style="FONT-STYLE: normal; DISPLAY: inline; FONT-FAMILY: 'Calibri'; COLOR: #000000; FONT-SIZE: small; FONT-WEIGHT: normal; TEXT-DECORATION: none"> <DIV style="FONT: 10pt tahoma"> <DIV> </DIV> <DIV style="BACKGROUND: #f5f5f5"> <DIV style="font-color: black"><B>From:</B> <A title=fernow@bnl.gov href="mailto:fernow@bnl.gov">Fernow, Richard C</A> </DIV> <DIV><B>Sent:</B> Monday, March 14, 2011 1:51 PM</DIV> <DIV><B>To:</B> <A title=MAP-l@lists.bnl.gov href="mailto:MAP-l@lists.bnl.gov">MAP-l@lists.bnl.gov</A> </DIV> <DIV><B>Subject:</B> Re: [MAP] Use of x,y,t as Hamiltonian coordinates.</DIV></DIV></DIV> <DIV> </DIV></DIV> <DIV style="FONT-STYLE: normal; DISPLAY: inline; FONT-FAMILY: 'Calibri'; COLOR: #000000; FONT-SIZE: small; FONT-WEIGHT: normal; TEXT-DECORATION: none"> <DIV class=WordSection1> <P class=MsoNormal><SPAN style="COLOR: #1f497d">Kirk,<o:p></o:p></SPAN></P> <P class=MsoNormal><SPAN style="COLOR: #1f497d"><o:p></o:p></SPAN> </P> <P class=MsoNormal><SPAN style="COLOR: #1f497d">First let me say that the physics content of ECALC9 is entirely the work of Gregg Penn. I made a modified version ECALC9F that took its input from an input file instead of the keyboard and have tried to maintain it as problems arose over the years. I also wrote the Mucool note 280 to help me understand what Gregg was doing. Sometimes this isn’t very clear in the code. I don’t think FORTRAN was Gregg’s native language. Anyway looking over the code again this morning<o:p></o:p></SPAN></P> <P class=MsoNormal><SPAN style="COLOR: #1f497d"><o:p></o:p></SPAN> </P> <P style="TEXT-INDENT: -18pt; mso-list: l0 level1 lfo1" class=MsoListParagraph><SPAN style="COLOR: #1f497d"><SPAN style="mso-list: ignore">1.<SPAN style="FONT: 7pt 'Times New Roman'">      </SPAN></SPAN></SPAN><SPAN style="COLOR: #1f497d">Greg calculates em6, emT, and emL using three different matrices.<o:p></o:p></SPAN></P> <P style="TEXT-INDENT: -18pt; mso-list: l0 level1 lfo1" class=MsoListParagraph><SPAN style="COLOR: #1f497d"><SPAN style="mso-list: ignore">2.<SPAN style="FONT: 7pt 'Times New Roman'">      </SPAN></SPAN></SPAN><SPAN style="COLOR: #1f497d">The variables for em6 are {x, y, t, px, py, E}. The momenta appear to be mechanical, i.e. the correction for Bz is not applied here.<o:p></o:p></SPAN></P> <P style="TEXT-INDENT: -18pt; mso-list: l0 level1 lfo1" class=MsoListParagraph><SPAN style="COLOR: #1f497d"><SPAN style="mso-list: ignore">3.<SPAN style="FONT: 7pt 'Times New Roman'">      </SPAN></SPAN></SPAN><SPAN style="COLOR: #1f497d">The variables for emT are {x, y, px, py}. The momenta also appear to be mechanical in this matrix. The statement I made about this at JLAB was apparently wrong.<o:p></o:p></SPAN></P> <P style="TEXT-INDENT: -18pt; mso-list: l0 level1 lfo1" class=MsoListParagraph><SPAN style="COLOR: #1f497d"><SPAN style="mso-list: ignore">4.<SPAN style="FONT: 7pt 'Times New Roman'">      </SPAN></SPAN></SPAN><SPAN style="COLOR: #1f497d">The variables for emL are {t, E, AT2}. The third variable is the square of the transverse amplitude.<o:p></o:p></SPAN></P> <P style="TEXT-INDENT: -18pt; mso-list: l0 level1 lfo1" class=MsoListParagraph><SPAN style="COLOR: #1f497d"><SPAN style="mso-list: ignore">5.<SPAN style="FONT: 7pt 'Times New Roman'">      </SPAN></SPAN></SPAN><SPAN style="COLOR: #1f497d">The only place where the on-axis field appears to be used is in calculating the canonical angular momentum and the transverse amplitude.<o:p></o:p></SPAN></P> <P class=MsoNormal><SPAN style="COLOR: #1f497d"><o:p></o:p></SPAN> </P> <P class=MsoNormal><SPAN style="COLOR: #1f497d">Rick<o:p></o:p></SPAN></P> <P class=MsoNormal><SPAN style="COLOR: #1f497d"><o:p></o:p></SPAN> </P> <P class=MsoNormal> <o:p></o:p></P> <DIV> <P class=MsoNormal><SPAN style="FONT-FAMILY: 'Arial','sans-serif'; FONT-SIZE: 10pt">It is my understanding the ICOOL/ECALC presently uses the first of these transformations, I.e., it uses coordinates</SPAN><o:p></o:p></P></DIV> <DIV> <DIV> <P class=MsoNormal><SPAN style="FONT-FAMILY: 'Arial','sans-serif'; FONT-SIZE: 10pt">(x, y, t, p_mech_x+qA_x/c, p_mech_y+qA_y/c, E_mech)<o:p></o:p></SPAN></P></DIV></DIV> <DIV> <P class=MsoNormal> <o:p></o:p></P></DIV> <DIV> <P class=MsoNormal><SPAN style="FONT-FAMILY: 'Arial','sans-serif'; FONT-SIZE: 10pt">[Rick Fernow: Can you comment on this?]</SPAN><o:p></o:p></P></DIV> <DIV> <P class=MsoNormal> <o:p></o:p></P></DIV> <DIV> <P class=MsoNormal><SPAN style="FONT-FAMILY: 'Arial','sans-serif'; FONT-SIZE: 10pt">It now seems to me that this is actually OK in principle (although perhaps a somewhat "ugly" transformation)</SPAN><o:p></o:p></P></DIV> <DIV> <P class=MsoNormal> <o:p></o:p></P></DIV></DIV> <P> <HR> _______________________________________________<BR>MAP-l mailing list<BR>MAP-l@lists.bnl.gov<BR>https://lists.bnl.gov/mailman/listinfo/map-l<BR></DIV></DIV></DIV></BODY></HTML>