The `Dispersion_relation` Component

A sample for magnon or phonon scattering based on numerical cross sections

Identification

Author: Daniel Lomholt Christensen and Kim Lefmann
Origin: NBI
Date: 22.06.23

Description

Single-cylinder shape.
Absorption included.
No multiple scattering.
No incoherent scattering emitted.
No attenuation from coherent scattering. No Bragg scattering.
Any crystal system: the unit cell is given either by its lengths and angles
(a, b, c, aa, bb, cc) or by its real-space lattice vectors (ax ... cz).



Algorithm:
0. Always perform the scattering if possible (otherwise ABSORB)
1. Choose a dispersion mode, a scattering point and a direction within a
focusing solid angle
2. Calculate the zeros of (E_i-E_f-hbar omega(kappa)) as a function of k_f
3. Choose one value of k_f (always at least one is possible!)
4. Perform the correct weight transformation

Dispersion files:
folder_path holds one file per dispersion mode. Each file has the columns
h  k  l  E  I
on a regular grid covering one unit cell in reciprocal lattice units: h, k, l
are the coordinates of q along the reciprocal lattice vectors a*, b*, c*,
h = a.q/(2 pi) and so on. For a cell with 90 degree angles and no vectors
given, a*, b*, c* lie along the sample x, y, z axes, as a, b, c do in
SpinWave_BCO and Phonon_simple. E [meV] is the mode energy and
I [barn/sr per unit cell of the given lattice] is the partial differential
scattering cross section of the mode, as the factor in front of the delta
function:
d2sigma/dOmega dE_f = (k_f/k_i) * DW * I(q) * n_B * delta(hbar omega - E(q)).
The component adds k_f/k_i, the Debye-Waller factor DW and the Bose factor
n_B = n(omega) + 1 for neutron energy loss and n(omega) for energy gain, so
I should not include them. I is looked up at the scattering vector folded
into the unit cell.

Weight:
p *= exp(-mu l) * dOmega * l_full * m * n_modes * rho_cell
* (k_f/k_i) * DW * I(q) * n_B * |dE_f/d(E(q) - |E_i - E_f|)|
with l the path length in the sample, dOmega the focusing solid angle,
l_full the path length without scattering, m the number of final
velocities found, n_modes the number of dispersion files and rho_cell the
density of unit cells.

Input parameters

Parameters in boldface are required; the others are optional.

Name	Unit	Description	Default
radius	m	Outer radius of sample in (x,z) plane.
yheight	m	Height of sample in y direction.
sigma_abs	barns	Absorption cross section at 2200 m/s per unit cell.
sigma_inc	barns	Incoherent scattering cross section per unit cell.
a	AA	Lattice constant, length of the a vector.	0
b	AA	Lattice constant, length of the b vector.	0
c	AA	Lattice constant, length of the c vector.	0
DW	1	Debye-Waller factor.
T	K	Temperature.
aa	deg	Angle alpha between b and c.	90
bb	deg	Angle beta between a and c.	90
cc	deg	Angle gamma between a and b with lengths and angles, a lies along x, b in the x-y plane and c completes a right handed set. With 90 degree angles, a, b, c lie along x, y, z.	90
ax	AA	x component of the real-space lattice vector a. If any of ax ... cz is non-zero, the vectors are used as given in the component frame and a, b, c, aa, bb, cc are ignored.	0
ay	AA	y component of a.	0
az	AA	z component of a.	0
bx	AA	x component of b.	0
by	AA	y component of b.	0
bz	AA	z component of b.	0
cx	AA	x component of c.	0
cy	AA	y component of c.	0
cz	AA	z component of c.	0
folder_path		Folder with one dispersion file per mode, see above.
target_x	m	position of target to focus at . Transverse coordinate.	0
target_y	m	position of target to focus at. Vertical coordinate.	0
target_z	m	position of target to focus at. Straight ahead.	0
target_index	1	relative index of component to focus at, e.g. next is +1.	0
focus_r	m	Radius of sphere containing target.	0
focus_xw	m	horiz. dimension of a rectangular area.	0
focus_yh	m	vert. dimension of a rectangular area.	0
focus_aw	deg	horiz. angular dimension of a rectangular area.	0
focus_ah	deg	vert. angular dimension of a rectangular area.	0
e_steps_low	1	Number of intervals the final velocity is searched in for roots on the energy loss side of the elastic line.	100
e_steps_high	1	Number of intervals on the energy gain side. Each interval holds at most one root, so two roots closer than an interval are missed: increase these for steep or crossing modes.	100
verbose	1	Prints information about the component if set to 1.	0

AT (	,	,		) RELATIVE
ROTATED (	,	,		) RELATIVE

The Dispersion_relation Component

Identification

Description

Input parameters

Links

The `Dispersion_relation` Component