Diana Shaul1, Henrique Araújo1, Daniel Hollington1, Alberto Lobo2, Markus Schulte1, Tim Sumner1, Simon Waschke1, Peter Wass3
1 Imperial College London; 2ICE/CSIC and IEEC; 3University of Trento
High energy cosmic ray and solar particle fluxes will charge up the LISA test masses (TMs). This charge will result in spurious electromagnetic forces acting on the TMs, disturbing their geodesic motion. The primary approach to minimise the impact of these forces is to discharge the TMs using the photoelectric effect. Unfortunately, the flux and energy spectrum of these high energy particles varies over time and therefore it is not easy to match charging and discharging rates, which would minimise the disturbances induced by charging. The gravitational reference sensor (GRS) can be used to measure the average charge accumulated, but not the shorter term variations in the charging rate. A radiation monitor (RM) can enable tracking of these changes.
We describe how a RM could be used to reduce the charging disturbances for LISA and the plans for use of the RM on LISA Pathfinder (LPF), including an approach that could enable acceleration noise associated with charging to be effectively subtracted.
- 2.3 Minimum Aims for RM on LPF
- Establish Monte Carlo (GEANT [4, 5, 12], FLUKA [13, 14, 15]) TM and RM charging simulation accuracy
- Establish approximate GCR and SEP transfer functions between RM and TM charge
- Establish/limit PSD of GCR flux and investigate whether there are any periodicities in the GCR flux in the LISA frequency band.
- Establish the SEP flux enhancements distributions (temporal and fluence) seen by RM
- Demonstrate the closed loop charge control process and estimate gain factor
- 2.4 Additional Aim for LISA: Derive TM charging rate and shot noise using RM
- Accurate measurement of RM-TM transfer function for net charging rate and charging noise could enable not only the coherent Fourier components but also charging shot noise to be effectively subtracted from the science data, as the RM would enable their independent and continuous measurement.
- This is an ambitious aim as there is a high level of ambiguity in the transfer function measurement. This is because it must be calibrated using the 2 direct measurements of the TM charging rate and shot noise, compared with the RM singles rate and the multi-channel coincidence deposited energy spectrum.
- To break the degeneracy, multiple measurements are needed in as diverse solar conditions as possible. On LPF, there is no real-time feedback between RM and GRS and hence this calibration may be limited due to the difficulty in predicting when a SEP will occur. However it should be possible for LISA.
- 2.4.1 Steps
- Start with a RM-TM transfer function derived from Monte Carlo models
- Recalibrate RM-TM transfer function in flight based on direct TM charging rate/noise measurements
- Ambiguity => iterate with each new direct TM measurement
- 2.4.2 Direct measurement: TM charging rate, shot noise
- The TM charging rate and shot noise may both be measured by applying a dither voltage to opposing electrodes and measuring the resultant TM displacement. 
- 2.5 RM improvements for LISA
- Electron monitor to track flux changes due to Jovian flux/early SEP warning
- Multiple, distributed RMs on LISA S/C to a/c for anisotropies in flux during SEP events, Forbush decreases etc..
- Real-time, on-board feedback between RM and GRS to: calibrate RM; match charging and discharging rates; to benefit from early SEP warning
- Improved spectral discrimination
- 1. INTRODUCTION
- 1.1 Charging Disturbances
- Charge on the TM leads to Coulomb and Lorentz forces from interactions with GRS conducting surfaces and IMF, respectively.
- These forces give rise to different types of disturbance:
- Acceleration noise, due to fluctuations in e.g. voltage 
- Modification of the effective stiffness describing TM-S/C coupling, due to position dependence of Coulomb forces 
- Coherent Fourier components, due to time dependence of the amount of charge on the TM [2,3]
- 1.2 The Incident Flux
- TM charging characteristics (net charging rate and charging shot noise) depend on the incident particle flux and its energy spectrum 
- Higher energy particles => higher charge multiplicity events => more noise and higher net charging rates, compared with lower energy particles 
- Solar Energetic Particle (SEP) energy spectra are softer than Galactic Cosmic Ray (GCR) spectra => A given particle flux will result in different TM charging characteristics, dependent on the proportion of SEP and GCR particles. 
- The charging disturbances will also depend on the variability of the incident flux over time. This may give rise to sharp or gradual changes or periodicities in the charging rate, potentially resulting in spectral leakage, modulation of the coherent Fourier components and the masking of true signals in the LISA bandwidth.
- Variations in flux:
- Solar Cycle: 11 year period; 50% difference in charging rate between solar minimum and maximum [4, 5]; Gradual and sharp changes possible 
- Solar rotation: ~ 27 day period; ~ 1 – 5 % GCR flux modulation 
- Jovian synodic year: 13 months; <5% TM charging rate modulation 
- SEPs: ~ 1 day–1 week; ~100-70000% (rare) TM charging rate increase 
- Forbush Decreases: ~days; ~ few – 35% GCR flux modulation. 
- Other GCR modulations: ~<few% in ~mins – week [8, 9]; Periodic fluctuations(?) [7, 10]
- 1.3 Charge Management
- Charge measurement: Apply dither voltages to opposing electrodes and measure resultant TM displacement => average charging rate. Accuracy depends on the dither voltage amplitude, dither frequency, degree of freedom, and integration time. Typically, an accuracy of 104e is reached in ~1 hour. This measurement does not give information on the charging shot noise nor the short term variability in the average charging rate.
- TM Discharge: Use UV light to discharge via the photoelectric effect. Nominal science mode: closed loop control to match charging and discharging rates as closely as possible, to minimise disturbances. 
- 2. THE RADIATION MONITOR
- 2.1 Aims
- Independent monitor of incident particle fluxes
- Minimise/track disturbances due to charging
- Help to manage disturbances
- Match charging/discharging rates
- Identify “DC” changes/coherent Fourier components
- Subtract Fourier components and charging noise
- 2.2 LPF RM Design
- (see e.g.  for more details)
- Shielding to mimic TM shielding
- Telescopic arrangement to enable SEP and GCR spectral discrimination within ~1hr for events registering in both diodes
- Minimum isotropic count rate >7c/s, set to ensure: recognise small changes in flux associated with e.g. SEPs; RM shot noise ~ TM charging shot noise; detect periodic modulation in flux before exceeds LISA noise
- Maximum count rate: large SEP: ~1500 c/s (isotropic), ~ 100 (coincident)
- Nominal time bin counter <30s (LPF: 1 mHz ≤ f ≤ 30 mHz)
Measurements = Synchronised GRS TM charging rate (noise) measurement with UV lamps off and acquisition of RM coincidence spectra
Scale the RM coincidence spectrum using the average RM singles rate over the same period.
Split the RM to TM charging noise transformation matrix into n segments, where n is the total number of direct TM charging rate (noise) measurements. The optimum positions of the segments will be derived using MC models.
Introduce n coefficients in the transformation matrix and solve for these coefficients, using the scaled coincidence spectra and direct TM charging measurements.
Repeat each time another suitable TM charging measurement is made to iteratively improve the transformation matrix.
To optimally improve this matrix, measurements should be made in as different solar conditions as possible.
- Schematic illustrating calibration of RM-TM transfer function
- Rough guide to LPF requirements for sensitivity and integration time for direct TM measurements in different solar conditions
2 Silicon PIN diodes in telescopic arrangement,
Example measurement accuracy for 1 day integration and dither voltage of 1V
Data : Coincidence spectrum, 10 mins integration
Singles rates, 10 secs integration
- N.B. It still needs to be confirmed whether the LPF RM spectral resolution is sufficient to distinguish variations in GCR spectrum during mission lifetime.
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