====== RT Improvement by Post-Processing ======

===== Basic Principle =====

  * bunch of charged particles excites damped oscillation in electronic circuit of the RT 
  * oscillation amplitude is proportional to total charge of particle bunch
  * existing GSI RT: signal fed to peak detector prone to noise at maximum position
  * large dynamic range: ~ 120 dB. 
  * typical resolution: ~10 pCRMS (6x10^7 protons)
  * for high current operation resolution drops to 100 nC (6x10^11 protons)

<color #ed1c24>-> insufficient e.g. for transmission control</color>

===== Bunch Charge determination =====

{{:bunch_charge_determination.png?direct&400|}}

[from: "A High Stability Intensity Monitoring System", M.A. Clarke-Gayther, RAL, Didcot (UK), presented on EPAC, Sitges (E) 1996]

{{:bild_zu_basic_principle.png?direct&400|}}

{{:bild_zu_bunch_charge.png?direct&400|}}

<color #7092be>Courtesy of A. Reiter</color>

===== Post-Processing of RT Oscillation Data =====

  * idea: : resonant frequency ω0 and decay time constant λ, are fixed by hardware
  * omission of inexact peak detector
  <color #ed1c24>-> improved RT resolution by digitization of oscillation data, FFT filtering and envelope fit </color>  

==== Algorithm for bunch charge determination ====

  * FFT filtering and offset correction
  * identification of maxima and minima until preset S/N value crossed
  * robust estimator of exponential decay curve 
  * evaluation of amplitude ~ total pulse charge

{{:bild1.png?direct&400|}}