Physics 736 Experimental Methods in Nuclear Particle and

Physics 736: Experimental Methods in Nuclear, Particle, and Astro Physics Prof. Vandenbroucke, March 18, 2015

HAWC technique

HAWC: High Altitude Water Cherenkov experiment • Construction recently completed: inauguration event this week • 4, 100 altitude meter site at Sierra Negra, Mexico (~19° N), near the Large Millimeter Telescope • 22, 000 m 2 area (57% coverage) • 300 water tanks (7. 3 m diameter x 4. 5 m depth) • 3 upward-facing 8’’ PMTs and one upward-facing 10’’ PMT (with high quantum efficiency) on the bottom of each tank • Sensitivity: 1 Crab (5 s) per day

First HAWC sky map

Announcements • Midterm – 24 hour take-home exam – Will be posted to Learn@UW today at 5 pm – Due tomorrow 5 pm in my office (Chamberlin 4114) – Cumulative on all subjects covered through last week – You are not allowed to work with other people – You are allowed to use books and the internet • Read Barlow Chapters 1 and 2 for Mon (Mar 23) • Read Barlow 3. 1 -3. 3 for Wed (Mar 25)

Time to digital converters • Time measurement is easier, more precise, less expensive than amplitude measurement • Useful for time over threshold (TOT) measurement: instead of measuring the pulse amplitude at a fixed frequency, set a threshold and measure the time that the pulse crosses above and the time that the pulse crosses below threshold • TOT is a rough proxy for pulse amplitude, and absolute times also valuable • Pulse amplitude estimate can be improved by using multiple TOTs with different thresholds • Compared to waveforms, data volume much smaller • Many channels can be implemented in single compact electronics module • Examples: used in Milagro, HAWC

Time over threshold / time to digital implementation • • Discriminator determines rising and falling edges Clock measures time between two edges Measurement is quantized to the clock tick size Measurement accuracy depends on clock resolution and stability

Counters/scalers • • • A scaler is a simple counter: count number of pulses in a time interval Instead of recording waveforms, amplitudes, or event pulse times Etymology: electromechanical counters had low number of bits, so circuits were used to divide (scale) the input pulse rate by a fixed factor (e. g. 100 or 1000) before incrementing Simple device: take digital pulses as input and increment register Can provide an output pulse when counter rolls over Faster and less expensive than ADCs and TDCs Appropriate for counting/monitoring high rates Two modes – Preset time: internal or external timer determines when readout occurs – Preset count: count until a certain counter value is reached (independently measure the elapsed time); advantage: constant statistical uncertainty can be chosen Important spec: Minimum time that can be resolved between leading edges (pulse pair resolving time) Can be used to monitor total rate per channel, in parallel with a more sophisticated DAQ system that provides more detailed information about multi-channel coincidence events Examples: HAWC low energy DAQ for gamma-ray bursts; Ice. Cube supernova DAQ

Ice. Cube supernova DAQ • For supernova neutrinos (~10 Me. V energy scale), inverse beta decay interactions are not bright enough to be detected by multiple DOMs (and distinguished from uncorrelated background photoelectrons) • Instead, a supernova can be detected through an increase in the individual DOM rates, correlated across the entire detector • This is monitored with scalers for individual DOM rates Simulation of 107 supernova neutrino interactions Time series of neutrino burst can be measured on top of steady noise floor

Aliasing and the Nyquist theorem • Given a set of discrete samples in a time series (e. g. from an ADC) • The same set of discrete samples can describe multiple possible high frequency input signals (aliases of one another) • Nyquist theorm: sampling frequency must be > 2 times the bandwidth (maximum frequency content) of the input signal • This can be achieved by including a low-pass filter before sampling a signal

Analog bandwidth vs. sampling frequency • An ADC is characterized by both quantities • Analog bandwidth due to response of circuit at high frequencies, before digital samples are determined • Typically the analog response rolls off at high frequency, perhaps intentionally for Nyquist sampling • To avoid ambiguity between sampling frequency and Nyquist frequency (sampling frequency / 2), “samples per second” is often used instead of hertz

Decibels • Logarithmic scale useful for quantifying amplitude/power of sine waves (sound, pressure, voltage, current, …) • Expressed as a ratio – Measured quantity relative to a standard reference – Output quantity relative to input quantity • Can be calculated with either amplitude or power: use factor of 10 for power and factor of 20 for amplitude so the result is the same • 3 d. B is a factor of ~2 in power • 20 d. B is a factor of 10 in amplitude (factor of 100 in power)

Low pass filters • • • Low pass RC circuit (“first order” filter) has characteristic shape Below critical frequency, gain = 1 At critical frequency, gain = -3 d. B (“ 3 d. B point”) Above critical frequency, response rolls off with a slope of 20 d. B per decade of frequency More stages can be added to provide sharper cutoff (higher order filter)

Flash/fast ADCs • • • Aka “direct conversion” ADC Brute force method: compare signal voltage to many different reference voltages using many different comparators and a resistor ladder Output of comparators is effectively a unary representation (aka “thermometer code”) and is converted to binary Advantage: fast (up to 3 GSamples/sec) because all bits determined in parallel, so can sample as fast as comparator and subsequent logic Disadvantages: high cost and power consumption and large physical size because for N bits of resolution, requires 2 N-1 comparators and voltage divider resistors Resistors must be precisely matched to one another for good differential nonlinearity In the worst DNL performance there are missing codes Can operate continuously (no dead time, no trigger required for digitization) Examples: used in Ice. Cube, VERITAS, MAGIC

ADC resolution: quantization error • 8 -bit ADC: resolution is 1/255 = 0. 4% • 12 -bit ADC: resolution is 1/4095 = 0. 02% • For flash ADCs, adding one bit of resolution doubles the number of components • For Wilkinson ADCs, adding one bit of resolution doubles the time to measure • Number of bits necessary should match signal to noise: not useful to digitize noise fluctuations • If large dynamic range is necessary, multiple ADC channels can be used in parallel, each with different gain

ADC resolution: effective number of bits • Noise effectively reduces the dynamic range • If you have 8 bits of ADC resolution but the noise level is greater than 1 leastsignificant bit, you effectively have lower resolution • Characterize by scanning input voltage over ADC range and measuring output • Convert measurement from ADC counts to measured voltage (will include total noise = quantization noise plus other noise) • The RMS of the deviation is the total (RMS) noise • If no other noise is present, RMS noise = quantization noise and effective number of bits = nominal number of bits • If measured noise is double that expected from quantization error, effective number of bits is decreased by 1 • In practice, noise might vary with input voltage and sampling frequency

Application-specific integrated circuits (ASICs) • Redundantly aka “custom ASICs” • A single chip (integrated circuit) is fabricated (in a large batch), optimized for the specific application • Not programmable like CPUs and FPGAs, but can have a large configuration space through control voltages and digital registers • Deterministic behavior given these configuration settings • For example, waveform sampling ASICs: sampling frequency, bandwidth, number of channels, memory depth etc. can be chosen for the specific application • Examples: ATWD, DRS, IRS, LABRADOR, TARGET, …

Example waveform readout design: Ice. Cube • Digitization locally inside each Digital Optical Module • Multiple waveform digitizer channels used: complementary range in amplitude (dynamic range) and time (sampling frequency) • Both ATWD and FADC are 10 bit • FADC: 40 MHz, 256 samples (6400 ns), no dead time, gain of 23 • ATWD (Analog Transient Waveform Digitizer): ASIC, 3 -channel (each with different gain) : 300 MHz, 128 analog samples (427 ns) stored in buffer and digitized upon request, dead time 32 -88 µs depending on number of channels digitized • 3 ATWD gains: 16, 2, 0. 25 • Two ATWDs used in “ping pong” mode: if one is busy the other can be used, for negligible overall dead time • Both digitizers triggered by discriminator with 0. 25 pe threshold

Example Ice. Cube waveforms Many photoelectron event Singe photoelectron event ATWD (high gain) ATWD (high gain channel) ATWD (medium gain) (ns) FADC ATWD (low gain) (ns)

Effects of cables (transmission lines) on signals Voltage drop Dispersion Time delay Reflections Strong effect on long cables (AMANDA, HAWC, radio astronomy, …) For precision timing applications, time delays are even important for short cables and traces on boards (0. 1 ns corresponds to 2 cm for n = 1. 5) • Cross talk: especially a challenge for fast signals near one another (e. g. traces on boards) • • •