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Time-of-flight measurement of ion energy

Time-of-flight measurement of ion energy. Tim Freegarde. Dipartimento di Fisica Università di Trento Italy. Time-of-flight measurement of ion energy. basic principles simple time-of-flight measurements and limitations spread-spectrum modulation linearity and nonlinearity

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Time-of-flight measurement of ion energy

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  1. Time-of-flight measurement of ion energy Tim Freegarde Dipartimento di Fisica Università di Trento Italy

  2. Time-of-flight measurement of ion energy • basic principles • simple time-of-flight measurements and limitations • spread-spectrum modulation • linearity and nonlinearity • pseudo-random sequences • transient (dynamical) problems

  3. Techniques for ion energy measurement • retarding field analysis ion signal ions Vr derivative ramp generator • Doppler spectroscopy spectrometer ions lens • time-of-flight chopper ions

  4. Principles of time-of-flight analysis chopper detector ions • take care to transform distributions correctly MODULATION FAST SLOW TOTAL time

  5. Modulation mechanisms • mechanical chopper balance hole trigger slit • electrostatic deflector / lens • product generation • laser, eg photolysis • pulsed source Vin

  6. Single pulse modulation CONVOLUTION • transmit short pulse of ions modulation true time-of-flight distribution • observed distribution is convolution of true distribution with modulating function = observed distribution • narrow pulse for good temporal resolution •  low signal: ions divided across distribution • modulation may be de-convoluted, but tends to amplify high-frequency noise

  7. Mathematical definitions • convolution (blurring) • correlation • Fourier transform • convolution theorem

  8. Frequency-domain analysis detector ions modulator time • measure {a(w),f(w)} as functions of modulation frequency w • time-of-flight distribution is given by

  9. variance of measured signal is - ie S/N = Acquisition time PULSED MODULATION • to measure time-of-flight distribution of duration with resolution at S/N ratio and incident ion flux we must run experiment for time SINUSOIDAL MODULATION • to measure single component at single frequency • we must run the experiment for time • for resolution over duration we must measure components • we must therefore run the experiment for a total time

  10. SPREAD-SPECTRUM MODULATION Spread-spectrum modulation • all frequencies present simultaneously in modulation function • phases adjusted so that components add in quadrature  flux at each frequency is • we therefore need only run the experiment for 20 frequencies random phases • truly random phases cause excursions out of range •  use pseudo-random functions

  11. Spread-spectrum history • Hedy Lamarr (1913-2000), George Antheil (1900-1959) patented submarine communication device • synchronized frequency hopping to evade jamming • original mechanical action based upon pianolas • used today in GPS, cellphones, digital radio http://www.ncafe.com/chris/pat2/index.html

  12. We COULD implement our spread-spectrum measurement by Spread-spectrum implementation • modulating the ion beam with a spread-spectrum function • analyzing both modulation and signal for frequency components • deriving the time-of-flight distribution from • However, if the modulating function is random – with d-function autocorrelation – then the time-of-flight distribution may be extracted more directly from • Autocorrelation of random modulating function of finite duration not quite zero • We therefore use ideal, ‘pseudo-random’ functions

  13. Linearity and saturation • nonlinearity • in deflector/modulator • due to saturation = + • nonlinearity generates harmonics of frequencies present • spread-spectrum techniques use simultaneous detection at different frequencies •  harmonics introduce false signals •  nonlinearity should be avoided… • • … or exploited: • binary modulation can’t distinguish nonlinearity •

  14. Binary pseudo-random sequences clock input Clock D SHIFT REGISTER 1 2 3 4 5 6 7 8 time • sequence length bits • with n bit shift register output AUTOCORRELATION  =

  15. Dynamically-induced effects electrostatic lens • signal detector aperture • voltage pseudo-random sequence • ions within lens element during transient see field-free change in potential •  lose or gain • two new velocity classes: • faster from 0-1 transition • slower from 1-0 transition

  16. Analysis of transient-induced signal pseudo-random sequence fast ion transient signal transient signal moved left • negative correlation transient signal moved right • positive correlation • contribution to ‘time-of-flight’ distribution: • additional correlations possible… time

  17. Time-of-flight measurement of ion energy • pseudo-random time-of-flight measurement reduces data accumulation time by factor over pulse modulation • simple pulse sequence generation • simple analysis by correlation • sensitive to nonlinearities and dynamic, transient effects • offers high resolution at lowest energies to complement retarding field energy analysis

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