User Guide

This guide gives an overview of NeSST’s main features and how to use them.

Quick Start

import NeSST as nst
import numpy as np

Primary Spectra

NeSST provides models for primary neutron spectra from DT, DD and TT fusion reactions.

Spectral Moments (Ballabio Fits)

The mean energy and variance of the primary neutron spectrum can be calculated using Ballabio fits (Ballabio et al. 1998, Nucl. Fusion 38 1723):

Tion = 3000  # ion temperature in eV (3 keV)

# DT primary spectrum moments
mean_DT, stddev_DT, variance_DT = nst.DTprimspecmoments(Tion)

# DD primary spectrum moments
mean_DD, stddev_DD, variance_DD = nst.DDprimspecmoments(Tion)

Primary Spectral Shapes

Two shapes are available for the primary spectrum:

Brysk (Gaussian): QBrysk()
Ballabio (modified Gaussian): QBallabio()

Ein = np.linspace(10e6, 18e6, 1000)  # energy array in eV
mean, _, variance = nst.DTprimspecmoments(Tion)

# Brysk (Gaussian) shape
I_E = nst.QBrysk(Ein, mean, variance)

# Ballabio (modified Gaussian) shape
I_E = nst.QBallabio(Ein, mean, variance)

Additionally, the DRESS Monte Carlo code can be used to generate primary spectra without assuming a particular shape:

Ein = np.linspace(10e6, 18e6, 200)  # energy array in eV

# DRESS DT primary spectrum, bin centres provided by Ein
I_E = nst.QDRESS_DT(Ein, Tion, n_samples = int(1e6))

Yields and Reactivities

Yield ratios between reactions can be estimated from reactivities:

dt_yield = 1e15
# DD yield predicted from DT yield
dd_yield = nst.yield_from_dt_yield_ratio("dd", dt_yield, Tion)
# TT yield predicted from DT yield
tt_yield = nst.yield_from_dt_yield_ratio("tt", dt_yield, Tion)

Scattered Spectra

The main feature of NeSST is calculating the singly-scattered neutron spectrum.

Setting Up Energy Grids and Scattering Matrices

Before computing scattered spectra, energy grids and scattering matrices must be initialised:

# Define energy grids
Eout = np.linspace(10e6, 16e6, 500)   # outgoing energy grid (eV)
Ein  = np.linspace(12e6, 16e6, 500)   # incoming energy grid (eV)

# Initialise DT scattering matrices
nst.init_DT_scatter(Eout, Ein)

Symmetric (Isotropic) Areal Density

For a spherically symmetric implosion:

I_E = nst.QBrysk(Ein, mean, variance)
total_spec, (nD, nT, Dn2n, Tn2n) = nst.DT_sym_scatter_spec(I_E)

Asymmetric Areal Density

For an asymmetric (anisotropic) areal density distribution:

# rhoL_func must be a function of cos(theta), normalised such that
# the integral over the sphere equals 1
rhoL_func = lambda x: np.ones_like(x)  # isotropic example

total_spec, components = nst.DT_asym_scatter_spec(I_E, rhoL_func)

Ion Kinematics

The effect of scattering ion velocities can be included:

# Ion velocity array
varr = np.linspace(-3e5, 3e5, 51)  # velocities in m/s

# Initialise scattering matrices with ion kinematics
nst.init_DT_ionkin_scatter(varr, nT=True, nD=True)

Transmission

The straight-line transmission of primary neutrons through the DT fuel can be calculated:

rhoL = 0.2    # areal density in kg/m^2
rhoL_func = lambda x: np.ones_like(x)

transmission = nst.DT_transmission(rhoL, Ein, rhoL_func)

Areal Density Conversion

Helper functions are provided to convert between areal density and scattering amplitude:

A_1S = nst.rhoR_2_A1s(rhoL)   # areal density -> scattering amplitude
rhoL = nst.A1s_2_rhoR(A_1S)   # scattering amplitude -> areal density

Fitting Models

The DT_fit_function class provides pre-built models for fitting experimental data:

E_DTspec = np.linspace(12e6, 16e6, 500)
E_sspec  = np.linspace(10e6, 16e6, 500)

fit = nst.DT_fit_function(E_DTspec, E_sspec)
fit.set_primary_Tion(Tion)
fit.init_symmetric_model()

# fit.model is a callable for use with scipy.optimize.curve_fit etc.

Neutron Time-of-Flight (nToF)

Synthetic nToF detector signals can be generated using the nToF class:

from NeSST.time_of_flight import nToF, get_unity_sensitivity, get_transit_time_tophat_IRF

distance = 3.0          # distance to detector in meters
sensitivity = get_unity_sensitivity()
IRF = get_transit_time_tophat_IRF(scintillator_thickness=0.01)

detector = nToF(distance, sensitivity, IRF)
t, t_norm, signal = detector.get_signal(Ein, I_E)

Materials

In addition to the default D and T materials, other materials can be initialised:

# Available by default: H, D, T, C12, Be9
mat = nst.init_mat_scatter(Eout, Ein, "C12")
rhoL_func = lambda x: np.ones_like(x)
spec = nst.mat_scatter_spec(mat, I_E, rhoL_func)

Publications

The models used in NeSST are described in:

1. Crilly et al., The effect of areal density asymmetries on scattered neutron spectra in ICF implosions, Physics of Plasmas, 2021
1. Crilly et al., Neutron backscatter edge: A measure of the hydrodynamic properties of the dense DT fuel at stagnation in ICF experiments, Physics of Plasmas, 2020