# Powder diffractometer curved Kaspar

Results of optimisation and simulation of curved powder diffractometer guide by Kaspar Hewitt Klenø

## Contents |

# 1 Introduction

## 1.1 Guide parameters and instrument layout

The guide is a an ellipse with a non-square cross section, curved in the horizontal place to eliminate the direct line of sight from the moderator to the sample. Maximum horizontal guide width (elliptical minor axis) is 2 cm. Maximum vertical guide width (elliptical minor axis) is 40 cm. The vertical focal points (relative to the beginning of the guide) are at -2.41 m and 154.215 m. The horizontal focal points (relative to the beginning of the guide) are at -80 m and 170.2 m (this means that the ellipse is stretched out to be almost straight (apart from the LoS-curvature)). The guide has a length of 153.5 m.

Top down view of the guide:

## 1.2 Notes on results

Since the design criteria for the instrument specified no limit for the vertical divergence in the integration box for the brilliance transfer as a function of wavelength, the integration box is naturally not fully illuminated at the source. This means the brilliance transfer as a function of wavelength goes above one. This is not a violation of Liouville's Theorem, as no part of the phase space density is increased; rather, parts of the phase space outside the specified integration box is transported to non-illuminated portions of the integration box, resulting in an integrated brilliance transfer above one. It is therefore useful to look at the brilliance transfer as a function of radial divergence, where the integration box is fully illuminated at the source, and thus the integrated brilliance transfer stays below one.

The beam spot size at the sample position has been left relatively lax in these simulations. This can be remedied by using a slit.

When comparing these results to the uncurved version (Powder_diffractometer_Kaspar), it can be seen that the curvature has a negligible effect on the transmission of the desired wavelengths. This is due the very high eccentricity of the horizontal ellipse, which allows for a very gentle curvature to break the LoS.

eps versions of the figures presented below are available at: http://guides.ess-scandinavia.dk/results/McStas/PostScript/curved_powder/

The raw data behind the figures presented below is available at: http://guides.ess-scandinavia.dk/results/McStas/Data/

# 2 Results with full bandwidth

## 2.1 1D monitors

Horizontal position

Vertical position

Horizontal divergence

Vertical divergence

## 2.2 Acceptance diagrams

Horizontal

Vertical

## 2.3 Brilliance transfer

As a function of wavelength

As a function of radial divergence

# 3 Snapshot results with 0.3 AA

## 3.1 1D monitors

Horizontal position

Vertical position

Horizontal divergence

Vertical divergence

## 3.2 Acceptance diagrams

Horizontal

Vertical

## 3.3 Brilliance transfer

As a function of wavelength

As a function of radial divergence

# 4 Snapshot results with 0.5 AA

## 4.1 1D monitors

Horizontal position

Vertical position

Horizontal divergence

Vertical divergence

## 4.2 Acceptance diagrams

Horizontal

Vertical

## 4.3 Brilliance transfer

As a function of wavelength

As a function of radial divergence

# 5 Snapshot results with 2 AA

## 5.1 1D monitors

Horizontal position

Vertical position

Horizontal divergence

Vertical divergence

## 5.2 Acceptance diagrams

Horizontal

Vertical

## 5.3 Brilliance transfer

As a function of wavelength

As a function of radial divergence

# 6 Snapshot results with 6 AA

## 6.1 1D monitors

Horizontal position

Vertical position

Horizontal divergence

Vertical divergence

## 6.2 Acceptance diagrams

Horizontal

Vertical

## 6.3 Brilliance transfer

As a function of wavelength

As a function of radial divergence http://guides.ess-scandinavia.dk/results/McStas/PNG/curved_powder/6AA/Liouville.sim.png6