Marco Panniello, Vittorio Giorgio Vaccaro, Naples. Mode Matching and Particle Studio* Comparison (with a little digression on the Wire Method) Marco Panniello, Vittorio Giorgio Vaccaro, Naples. Carlo Zannini, CERN. * Particle Studio with the new filtering tool

Not reliable region, dependent by bunch length Particle Studio The results from Particle Studio seem almost insensitive to the conductivity and going up in frequency, the reliability is clearly bad. We need a shorter bunch (and then a very thin mesh) to investigate the red frequency region. σ=1mm Wake-length (WL)=3m Not reliable region, dependent by bunch length s Gaussian bunch adopted as excitation signal

Particle Studio & Mode Matching Without take care of the bunch and the wakefield length there is an acceptable agreement only from 2.4 to 6.0 nwn. To reach better results, a shorter bunch (σ) and longer “wake” (WL) are needed. The bunch length and the WL must be chosen accurately during the simulation setup, to obtain reliable results by PS. σ=1mm Wake-length (WL)=3m Bad agreement region, dependent by bunch length in PS simulations.

Particle Studio & Mode Matching Below cutoff, there is agreement on the resonant frequency values, but not on the peaks height. The WL determines a upper limit for the Quality Factor. σ=1mm Wake-length (WL)=3m

Particle Studio & Mode Matching Changing the geometrical parameters, the remarks on the comparison between the behaviour of the two codes are the same. In the next slide it is shown the first resonance magnification for two different values of the conductivity. σ=2mm Wake-length (WL)=3m Bad agreement region, dependent by bunch length in PS simulations.

Particle Studio & Mode Matching Wake-length (WL)=3m

Particle Studio & Mode Matching The peak of the impedance from PS seems be constant to 2.9 kΩ, while the MM results scale according to the square root of the conductance ratio.

Particle Studio & Mode Matching Pillbox: b = 15 mm; c = 43 mm; 2L = 30 mm; βγ > 1000; Conductance [S/m] Re(Zc) [kΩ] Q QSF Re(Zc/Q) [Ω] f 0 [GHz] fSF [GHz] (PEC) 6∙105 MM 62 1808 1427 68.6 2.761 2.760 103 MM 2.6 72 58 70.3 2.798 6∙105 PS 2.9 56 103 2.754 103 PS 60 96.7 Remark: the values of the impedance peaks calculated by MM are proportional to the square root of the conductance ( ) ; The impedance calculated by means of PS without opportune trick, seems to be constant.

A reliable Q factor by Particle Studio Increasing the WL, the accuracy in the frequency domain results improved. The accuracy is fundamental if we are interested to determine the Q and the impedance peak. Otherwise, to determine only the modes resonant frequency, it is sufficient a very short wake because it is important only to excite the modes . Every simulation stops at some time. This means that the signals that are calculated are truncated at this point, regardless of their values. If these values are non-zero, the Fourier Transformation will produce an error because only a part of the ”whole” signal with all of its non-zero values has been used for the transformation. Therefore, the ”smaller” the signals are, the more accurate the frequency domain values will be.

A reliable Q factor by Particle Studio Time and memory needed to simulate a lossy pillbox (b = 15 mm; c = 43 mm; 2L = 30 mm;), by a standard PC. It is worth of note, the large amount of memory needed to reach a relatively little Q value. WL [m] Time [s] Memory [Mb] Qsim Qmax 12 120 46 107 110 30 480 88 253 275 60 1440 157 461 550 4680 296 761 1100 300 25920 711 1149 2750 1000 ? >1400 9167

A reliable Q factor by Particle Studio Qsim versus Qmax of the first resonance peak, for different conductivity values. The PS simulations tend to the SF results as the Qmax increases. For very high conductivity, PS need an unacceptable amount of time and computer memory, to allow a practical employment.

A reliable Q factor by Particle Studio SX. Qsim versus Qmax of the first resonance peak, for a PEC pillbox. DX. Qsim versus resistivity, on changing the WL value.

Conclusions Particle Studio is able to effectively operate in frequency domain. In the case of resistive wall structures (e.g. steel or Copper), it is necessary to simulate very long wakes in time domain to obtain reliable results for the Q factor. It means to perform simulations that need a large amount of computer memory and excessive time to be accomplished. These characteristics are more evident if compared to Mode Matching Technique performances.

Real model & Virtual Measurements b=10;c=30;2L=20 Steel pillbox --------------- exact evaluation --------------- Virtual measurement

Real model & Virtual Measurements

Real model & Virtual Measurements For this peak we performed simulations varying the wire radius. The results are reported in the next slide

Real model & Virtual Measurements (Approaching the Real Model) Reducing the wire radius the results tend to the resonance of the real model. In order to converge, the radius becomes unfeasible.