KATRIN ToF Simulations and Analysis Alexander Fulst 15th February 2016 Table of Contents 1 KATRIN 2 Idea of ToF measurements 3 SDS II measurements Measurement plan Measurement execution 4 Simulations Prerequisites Proof of Concept First Results 5 Summary and Outlook Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 2 KATRIN KATRIN KArlsruhe TRItium Neutrino Experiment Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 3 KATRIN Neutrinos have a finite mass Figure: Zenith angle distribution of e-like and µ-like events in Super-Kamiokande with momenta above and below 1.33 GeV with expectation (boxes) and best fit (lines) [1] Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 4 KATRIN Neutrinos have a finite mass Figure: Zenith angle distribution of e-like and µ-like events in Super-Kamiokande with momenta above and below 1.33 GeV with expectation (boxes) and best fit (lines) [1] Nobel Prize in Physics 2015: T. Kajita and A. McDonald Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 4 KATRIN Neutrinos have a finite mass Figure: Zenith angle distribution of e-like and µ-like events in Super-Kamiokande with momenta above and below 1.33 GeV with expectation (boxes) and best fit (lines) [1] Nobel Prize in Physics 2015: T. Kajita and A. McDonald Alexander Fulst KATRIN ToF Simulations and Analysis only gives ∆m2 , no absolute scale 15th February 2016 4 KATRIN Overview over KATRIN Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 5 KATRIN Overview over KATRIN direct determination of ν̄e mass (incoherent sum over mass eigenstates) endpoint of e − -spectrum from 3 H → 3 He+ + e − + ν̄e decay Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 5 KATRIN Overview over KATRIN direct determination of ν̄e mass (incoherent sum over mass eigenstates) endpoint of e − -spectrum from 3 H → 3 He+ + e − + ν̄e decay Figure: β-spectrum of tritium [2] needed: strong source, high acceptance, low background Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 5 KATRIN Overview over KATRIN direct determination of ν̄e mass (incoherent sum over mass eigenstates) endpoint of e − -spectrum from 3 H → 3 He+ + e − + ν̄e decay Figure: β-spectrum of tritium [2] needed: strong source, high acceptance, low background upper limit of ≈ 0.2 eV (90% C.L.), mν = 0.35 eV: 5σ Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 5 KATRIN Figure: schematic setup of KATRIN (a) Rear Section (b) WGTS (1011 Bq) (c) DPS (d) CPS (total reduction of gas flow by 1012 ) (e) Pre-Spectrometer (f) Main Spectrometer (energy resolution of 0.93 eV) (g) Detector Section Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 6 KATRIN Figure: layout and working principle of a Magnetic Adiabatic Collimation combined with an Electrostatic (MAC-E) filter adiabatic: magnetic moment µ = energy resolution: Alexander Fulst ∆E E = E⊥ B is constant Bmin Bmax KATRIN ToF Simulations and Analysis 15th February 2016 7 Idea of ToF measurements Idea of ToF measurements Time-of-Flight Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 8 Idea of ToF measurements Simple ToF Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 9 Idea of ToF measurements Simple ToF measuring the time-of-flight of particles gives information about their energy Figure: differential ( dN dE (E ), left) and integrated (Ṅ(qU), right) spectrum [4] Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 9 Idea of ToF measurements Simple ToF most simple case: non-relativistic non-accelerated motion v= q Alexander Fulst 2Ekin m ⇒t= qs 2Ekin m KATRIN ToF Simulations and Analysis 15th February 2016 10 Idea of ToF measurements Simple ToF most simple case: non-relativistic non-accelerated motion v= q 2Ekin m ⇒t= qs 2Ekin m in KATRIN electrons get slowed down/accelerated in the main spectrometer furthermore: electrons have different pitch angles to B-field, cyclotron motion causes longer ToF Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 10 Idea of ToF measurements Figure: ToF for simulated electrons with standard KATRIN setup Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 11 Idea of ToF measurements Figure: ToF for simulated electrons with standard KATRIN setup Problem start signal needed to measure ToF Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 11 Idea of ToF measurements Figure: ToF spectrum for different neutrino masses at 18570 eV retarding potential and 18574 eV endpoint energy [3] Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 12 Idea of ToF measurements Time Focusing Time-of-Flight (tfToF) most simple solution is a gated filter periodic blocking of continous beam gives small start window sensitivity of σstat (mν2e ) = 0.021 eV2 compared to standard σstat (mν2e ) = 0.020 eV2 [3] Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 13 Idea of ToF measurements Time Focusing Time-of-Flight (tfToF) most simple solution is a gated filter periodic blocking of continous beam gives small start window sensitivity of σstat (mν2e ) = 0.021 eV2 compared to standard σstat (mν2e ) = 0.020 eV2 [3] use time-varying potential to accelerate electrons Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 13 Idea of ToF measurements Time Focusing Time-of-Flight (tfToF) most simple solution is a gated filter periodic blocking of continous beam gives small start window sensitivity of σstat (mν2e ) = 0.021 eV2 compared to standard σstat (mν2e ) = 0.020 eV2 [3] use time-varying potential to accelerate electrons electrons arriving later are accelerated more than electrons arriving early, comparable to bunching in accelerators Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 13 Idea of ToF measurements Time Focusing Time-of-Flight (tfToF) most simple solution is a gated filter periodic blocking of continous beam gives small start window sensitivity of σstat (mν2e ) = 0.021 eV2 compared to standard σstat (mν2e ) = 0.020 eV2 [3] use time-varying potential to accelerate electrons electrons arriving later are accelerated more than electrons arriving early, comparable to bunching in accelerators periodicity of potential change also gives a start signal Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 13 SDS II measurements SDS II measurements Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 14 SDS II measurements Figure: concept of tfToF Main Spectrometer setup Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 15 SDS II measurements Measurement plan What does the potential in the spectrometer look like? one cannot directly measure the real applied voltage on the inner electrodes egun needed to analyze the potential Figure: Kepco input vs output Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 16 SDS II measurements Central Part 5 rings connected ring 7-11 ring 6 Flat Cone 3 rings wire layer wire layer ring 5 Outer Inner Main Spectrometer vessel ring 4 ring 3 Steep Cone 2 rings ring 2 390kΩ 2x200V ... HV distribution rack ... +500V 2x22 Single channel offset supplies ISEG EHS 8205 IE common west -1kV Dipole supply FuG HCV 2M-1000 IE common east Dipol east Dipole west e-gun HV cage IE common -2kV ISEG NHQ 122m External supplies IE Global Offset North -35kV FuG HCN 140M35000 Triode Protection board Wire electrode Ring 12 – 16 Inner and Outer Wire Layer 50 4.7nF E-gun LED 50 Channel 21 Patch Panel West Tektronix function generator 3102 + Sync Out - + - Patch Panel East Amplifier Kepco BOP 1000M Agilent function generator 33220A + Sync - + Out - 230V Supply 2V Supply + In - + Out - Supply Vessel Potential -18.4kV Figure: standard (top) and pulsed-cone tfToF (bottom) HV setup Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 17 SDS II measurements Measurement execution Measurement execution Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 18 SDS II measurements Measurement execution Measurement execution 30 Agilent pulser as master with rate of 1 kHz (provides waveform for Kepco and trigger for egun pulser) ra mp ed vo lta g e [V] 20 10 0 −10 −20 −30 0 200 400 600 800 1,000 time [ μs ] Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 18 SDS II measurements Measurement execution Measurement execution 30 Agilent pulser as master with rate of 1 kHz (provides waveform for Kepco and trigger for egun pulser) ra mp ed vo lta g e [V] 20 10 0 −10 −20 −30 0 200 400 600 800 1,000 time [ μs ] egun pulser at 24 kHz means 42 µs pulse period and 15 ◦ phase shift between pulses 24 egun pulses per cycle, electron ToF is expected to be less than 25 µs Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 18 SDS II measurements Measurement execution Measurement execution 30 Agilent pulser as master with rate of 1 kHz (provides waveform for Kepco and trigger for egun pulser) ra mp ed vo lta g e [V] 20 10 0 −10 −20 −30 0 200 400 600 800 1,000 time [ μs ] egun pulser at 24 kHz means 42 µs pulse period and 15 ◦ phase shift between pulses 24 egun pulses per cycle, electron ToF is expected to be less than 25 µs for finer scanning, measurements are repeated for phase shifts from 0 ◦ to 13.5 ◦ in 1.5 ◦ steps this results in 240 pulses during a waveform of 1000 µs Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 18 SDS II measurements Measurement execution Measurement execution 30 Agilent pulser as master with rate of 1 kHz (provides waveform for Kepco and trigger for egun pulser) ra mp ed vo lta g e [V] 20 10 0 −10 −20 −30 0 200 400 600 800 1,000 time [ μs ] egun pulser at 24 kHz means 42 µs pulse period and 15 ◦ phase shift between pulses 24 egun pulses per cycle, electron ToF is expected to be less than 25 µs for finer scanning, measurements are repeated for phase shifts from 0 ◦ to 13.5 ◦ in 1.5 ◦ steps this results in 240 pulses during a waveform of 1000 µs whole procedure repeated for different surplus energies from 0 eV to 5 eV in 0.5 eV steps Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 18 SDS II measurements Measurement execution tfTOF spectrum (phase-aligned, shifted AP, 50 V tf amplitude) 300 phase = 0.0°, energy = 1.0 phase = 4.5°, energy = 1.0 electron count 250 200 150 100 50 0 0 200 400 time of arrival [us] 600 800 1000 Figure: 0 ◦ and 4.5 ◦ waveform scanning for surplus energy of 1 eV Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 19 Simulations Simulations Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 20 Simulations Prerequisites Prerequisites Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 21 Simulations Prerequisites Prerequisites Kassiopeia framework brings nearly everything needed for simulation... Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 21 Simulations Prerequisites Prerequisites Kassiopeia framework brings nearly everything needed for simulation... ... but does not support time-varying potentials! Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 21 Simulations Prerequisites Prerequisites Kassiopeia framework brings nearly everything needed for simulation... ... but does not support time-varying potentials! there was the idea to multiply the calculated field with a time-dependent factor Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 21 Simulations Prerequisites Prerequisites Kassiopeia framework brings nearly everything needed for simulation... ... but does not support time-varying potentials! there was the idea to multiply the calculated field with a time-dependent factor this idea was picked up and extended to use two different pre-calculated fields A and B i.e. α(t) · A + (1 − α(t)) · B (e.g. α(t) = 0.5 + 0.5 sin (ω · t)) Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 21 Simulations Prerequisites Prerequisites Kassiopeia framework brings nearly everything needed for simulation... ... but does not support time-varying potentials! there was the idea to multiply the calculated field with a time-dependent factor this idea was picked up and extended to use two different pre-calculated fields A and B i.e. α(t) · A + (1 − α(t)) · B (e.g. α(t) = 0.5 + 0.5 sin (ω · t)) −40 −50 potential [V] −60 −70 −80 −90 −100 −110 −200 0 200 400 600 800 1,000 1,200 t i me [ μs] Figure: concept of using two fields and interpolating between them Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 21 Simulations Proof of Concept Proof of Concept Figure: simple oscillation test setup to show time-dependent fields Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 22 Simulations Proof of Concept Figure: simple transmission test setup to show time-dependent fields Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 23 Simulations Proof of Concept 1.0 transmission probability 0.8 0.6 0.4 0.2 0.0 100 fit: 1.00-0.88*sin(1.00*2pi/1000) simulated data 0 100 200 300 400 500 600 start time in ms Figure: transmission probability over time Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 24 Simulations First Results 0.1 eV surplus energy 70 60 counts 50 40 30 20 10 0 0 200 400 600 800 1000 time of arrival / us tfTOF spectrum (phase-aligned, shifted AP, 50 V tf amplitude) 300 phase = 0.0°, energy = 1.0 phase = 4.5°, energy = 1.0 electron count 250 200 150 100 50 0 0 200 400 time of arrival [us] 600 800 1000 Figure: full waveform scanning for surplus energy of 0.1 eV surplus (simulated, top) and 1 eV (bottom, measured) Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 25 Simulations First Results 0.5 eV surplus energy 1400 1200 counts 1000 800 600 400 200 0 10 15 20 25 30 35 25 30 35 time of flight / us 2.0 eV surplus energy 3000 2500 counts 2000 1500 1000 500 0 10 15 20 time of flight / us Figure: ToF spectrum for 0.5 eV (top) and 2.0 eV (bottom) surplus energy Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 26 Simulations First Results 1.0 eV surplus energy, 0.0° phase shift 800 700 600 counts 500 400 300 200 100 0 10 11 12 13 14 15 time of flight / us Figure: ToF distribution in dependence of start time for 1.0 eV surplus, blue: first 500 µs, red: 500 − 1000 µs Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 27 Summary and Outlook Summary and Outlook Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 28 Summary and Outlook Summary and Outlook Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 29 Summary and Outlook Summary and Outlook time-varying fields have been implemented and work as intended Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 29 Summary and Outlook Summary and Outlook time-varying fields have been implemented and work as intended simulations look good at the first glance Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 29 Summary and Outlook Summary and Outlook time-varying fields have been implemented and work as intended simulations look good at the first glance open questions for measured data (shift and background/phase effects) Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 29 Summary and Outlook Summary and Outlook time-varying fields have been implemented and work as intended simulations look good at the first glance open questions for measured data (shift and background/phase effects) next steps: identify peaks in measured data and analyze them find the waveform best matching the data optimize waveform to use for real measurements Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 29 Summary and Outlook Thank you for your attention Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 30 Summary and Outlook Literatur und Abbildungen Y. Ashie et al.: ”Measurement of atmospheric neutrino oscillation parameters by Super-Kamiokande I”, in Phys. Rev. Lett. D71, 112005 (2005) KATRIN homepage http://www.katrin.kit.edu/79.php as of 10.02.2016 N. Steinbrink et al.: ”Neutrino mass sensitivity by MAC-E Filter based time-of-flight spectroscopy with the example of KATRIN”, in New Journal of Physics 15 (2013) 113020 M. Kleesik: ”A Data-Analysis and Sensitivity-Optimization Framework for the KATRIN Experiment”, PhD thesis (2014) Alexander Fulst KATRIN ToF Simulations and Analysis 15th February 2016 31
