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Complex Analysis of Askaryan Radiation: A Fully Analytic Model in the Time…

- - - - 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
- - - - Fully analytic: RB
        
        Semi-analytic: ARVZ, ARZ, etc.
        
        NuRadioMC
  - - - 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
      - Definition of eta, definition and justification of omega_C, f_C
      - "All theta, all omega" vs. "all theta, all t"
    - - 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)"
    - - Derivation from form factor and RB equations (draw from last paper but correct errors)
        
        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)
        
        Omega_C
        
        a (Energy)
        
        Pulse width (cutoff-frequencies)
        
        rho_0 (quantum mechanics)
        
        Amplitude
        
        R E (energy)
        
        Discuss 3-variable scan
    - - Derivation from form factor and RB equations
        
        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
        
        Discuss observables
        
        Pulse width: delta-theta and a
        
        First scan theta, a (x-axis correlation)
        
        Obtain constant pulse-width
        
        2 more items...
    - - Describe procedure
        
        Digitization
        
        Resampling and smoothing
        
        Graphs and Tables
        
        On-cone
        
        Graph: display fits, Table of fit parameters
        
        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
        
        1 more item...
        
        Off-cone
        
        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
        
        1 more item...
    - - Three ways this can be used
        
        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