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 retarding field analysis Techniques for ion energy measurement Doppler spectroscopy time-of-flight VrVr ramp generator ions ion signal derivative ionslens spectrometer ions chopper

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

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

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

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

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

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

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

11 Spread-spectrum history Hedy Lamarr ( ), George Antheil ( ) patented submarine communication device synchronized frequency hopping to evade jamming original mechanical action based upon pianolas used today in GPS, cellphones, digital radio

12 Spread-spectrum implementation We COULD implement our spread-spectrum measurement by 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 -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 generates harmonics of frequencies present =+ nonlinearity in deflector/modulator due to saturation spread-spectrum techniques use simultaneous detection at different frequencies harmonics introduce false signals nonlinearity should be avoided… … or exploited: binary modulation cant distinguish nonlinearity

14 Binary pseudo-random sequences D Clock SHIFT REGISTER time clock input output sequence length bits with n bit shift register = AUTOCORRELATION

15 Dynamically-induced effects electrostatic lens detector aperture voltage signal 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 slowerfrom 1-0 transition

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

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