Complex Analysis of Askaryan Radiation: A Fully Analytic Model in the Time-Domain
Abstract flow-down
UHE-nu detections
Askaryan-class detectors
Prior work: fully analytic model, 3D form factor, LPM elongation (all omega, all theta)
On-cone analytic model in the time-domain
Extend to all time, all theta
Explain features: tied to physical parameter space
Comparison to NuRadioMC and semi-analytic results
Introduction
Astroparticle physics and the Askaryan Effect
RICE, ANITA, ARIANNA, ARA, IceCube-Gen2
LOFAR, AERA
Lines of Work
MC: ZHS and others
Fully analytic: RB
Semi-analytic: ARVZ, ARZ, etc.
NuRadioMC
Section outline
Units, definitions, and conventions
Derivation of the form factor
Opening diagram geometry: viewing angle, cascade length and width
Definition of the 3D Fourier transform, and form factor
Discussion of cascade maximum, cascade width and how it relates to energy
Units of normalizing factors
Apply the definition
Quote the current and the function f(x,t)
Cite the prior paper to justify definition
Provide example (appendix?) of ZHS form factor and GEANT4
Compare to analogue filter theory, define omega_CF and omega_0, f_CF and f_0
Include here the derivations of "a ~ ln(E/E_crit)"
On-cone field equations
Derivation from form factor and RB equations (draw from last paper but correct errors)
Definition of eta, definition and justification of omega_C, f_C
Graph: basic E-field with varying epsilon (normalized) Illustrate the asymmetry potential, and compare and contrast to -dA/dt of ARVZ
Discuss observables
Asymmetry (epsilon)
Pulse width (cutoff-frequencies)
Amplitude
Off-cone field equations
Derivation from form factor and RB equations
"All theta, all omega" vs. "all theta, all t"
Graph: basic E-field with varying cutoff frequencies and viewing angles (normalized) Illustrate the role of p (pulse width), and theta-dependence with several cutoff frequencies
Omega_C
R E (energy)
a (Energy)
rho_0 (quantum mechanics)
Discuss observables
Pulse width: delta-theta and a
First scan theta, a (x-axis correlation)
Obtain constant pulse-width
Next, scan w_0 and E
Discuss error estimation
Discuss 3-variable scan
Comparison to semi-analytic parameterizations
Describe procedure
Digitization
Resampling and smoothing
Graphs and Tables
On-cone
Off-cone
Graph: display fits, Table of fit parameters
Graph: display fits, Table of fit parameters
Graphs: cascade-a vs. theta off-cone
Describe fit procedure: correlation with cascade-a and theta (x-axis), then sum-squares with E and omega_0
quote results in table, waveform parameters, and correlation and power %, include cascade-a from Gaussian fits
Graphs: f_0 vs. f_C
Describe fit procedure: since we know theta = theta_C, just a 3-level loop over omega_C, omega_0, and E
Just minimizing sum-squares
quote results in table, waveform parameters, and correlation and power %, include cascade-a from Gaussian fits
Conclusion
Three ways this can be used
Restrict to case in which theta is already known
Graph of a (waveform) vs. a (fit from Gaussian)
First, when analytic models are
matched to observed data, cascade properties may be calculated directly from single RF waveforms.
Second, fully analytic models require no Monte Carlo simulation of cascade particle trajectories,
minimizing computational intensity.
(Some assessment of speed or O(N) computational complexity?)
Third, fully analytic models can be embedded in firmware to
enhance the real-time sensitivity of detectors.
Diagram of the idea
Thermal noise rejection power (maybe scan and correlate to Gaussian white noise)
Summary
Thank those involved
Quote major results in a Table
Subsection about uncertainty principle