Cascade Review 3/2/2011

NIM CLIC CRAB paper – practically finished….awaiting final author approval/comments  Draft awaiting final submitting procedure on the NIM website before it can be sent to reviewers  I have contacted all the authors concerned with the paper:  Have done Graeme’s corrects (typo’s mostly)  Andy Wolski changes:  1) replace BDS table (pg 2) with Beta function plot instead  2) although the bunch length is small for the GUINEA-PIG calculation both x’ and z’ should be transformed as well  3) Section 3 (which describes the testing process in great detail) he feels should be replaced with a simple explanation (a few paragraphs) describing the tests preformed – since from his point of view it adds little to the paper i.e. “kept it concise and to the point” I will still have 5 pages (2 to 3 pages removed).  So basically this paper is done… apart from any comments from Dr Jones with regards to the current draft?  Have begun next step with James Jones regarding the tuning of the magnets/Crab to fix problems sited in the paper (this will be a separate paper in it’s own right)….start calculations next week?

Mode Matching NIM to do list  Most the results for TM modes (theory and results) already exist  12 section paper – Results that already exist  GSM for field determination – Theory done, Program done – benchmark against CLIC ZC2 WNW and curved geometry  Dispersion curve analysis – Theory done, Program done – benchmark against CLIC ZC2 WNW and curved geometry  Rapid cavity optimisation – Theory done, Program done – benchmark against CLIC ZC2 WNW and curved geometry  Results Yet to do  Include coaxial modes so that a simulated stretched wire measurement can be made – Theory in progress, scalar product for TM to TEM and TM to TM done, but benchmark not finished.  Derive fields for Coaxial section  Use GSM to obtain longitudinal impedance of structure  Once the last point has been achieved then I can use my pre-existing programs techniques to obtain the Kick factors and hence the Wakefields of the structure (above cut- off)

Mode Matching NIM Coaxial progress….  Coaxial cascading still does not agree with HFSS  I am checking my Matrices against the MATHEMATICA solution of the integrals (maybe a mistake is there somewhere)…or might possibly be problem in coding or how I have included the TM to TM matrix into the TM to TE…..  Comparing the Matlab analytically entered matrices to those generated by Mathematical

Is it the Bessel Neumann roots? MatlabRootX0Value=10^-015 { , , , , , }  Comparing the residual from the numerical implementation of the roots calculated in Matlab and those in Mathematica results in ~0 i.e. the roots are correct for all intensive purposes  So this is not the issue

Is it the Coaxial TM into TEM mode scalar product? (*Matlab output*) MATLABanmTEMTM={ , , , , , }  Comparing manually integrate integrals to those of both the analytical and numerical integration in Mathematica results in the same answer for TM into TEM scalar product  Hence this is not the issue….

Is it the Coaxial TM into TM scalar product?  Comparing manually integrate integrals to those of both the analytical and numerical integration in Mathematica results in the same answer for TM into TEM scalar product.  There are different ways in which the problem can be approached.

Direct integration of the coaxial TM into TM scalar product  A direct integration of the equations within Mathematica, without any bounds, gives erroneous results i.e. numerical errors – don’t do it this way…

Direct integration of the coaxial TM into TM scalar product with bounds  Directly applying the output equation (with bounds) to the problems generates the TMTM scalar product matrix for the coaxial line

Direct integration of the coaxial TM into TM scalar product with bounds output:  The above scalar product should be the same as that obtained by expansion of the TMTM equation, followed by Bessel function manipulation and then integration – which is the approach used by L.Carin

Direct integration of the coaxial TM into TM scalar product L.Carin approach  The results obtained by this method are the same as those I obtained by integrating by hand i.e. pad and paper and then implementation into Matlab…

 The results are in agreement  However these are different to the other method… Direct integration of the coaxial TM into TM scalar product L.Carin approach Matlab and Mathematica comparison

Coaxial TM into TM scalar product comparison Direct integration with bounds L.Carin method

Other things to check….  1)Impedance matrices  2)The implementation of the NW coaxial region  3)How the TMTEM is incorporated into the final coaxial scalar product matrix..