6. Nozzle design evaluation using CFD model Three of the nozzle’s key design parameters have

been changed to investigate their effect on gas flow:

the diameter of the throat D2, the diameter of

divergent end D3, and the depth of the divergent path

h3 (Figure 10).

Analysis of nozzle design used for reducing the MSF errors in rapid plasma figuring Nan Yu*, Renaud Jourdain, Mustapha Gourma, Paul Shore

2. Research motivations

Fig. 1 Large telescope Fig. 2 EUV-lithography Fig. 3 Fusion energy Fig. 4 Space observer

Ground-breaking science programmes and research projects, such as European

Extremely Large Telescope (EELT), Extreme Ultraviolet (EUV) lithography systems, laser

fusion energy plants, and compact space based observers, require metre-scale optics.

Thus this research focuses on an advanced optical finishing fabrication technique for

large and ultra-precise surfaces.

1. Introduction This project is about the design, fabrication, and characterisation of novel Inductively

Couple Plasma (ICP) torch nozzles. These nozzles will enable the creation of highly

collimated energy beams characterised by a material removal footprint of a few

millimetre in diameter. This dedicated plasma technology will be used through a dwell

time figuring method for the correction of large optical surfaces.

3. Research target 1. Form accuracy: < λ/60 RMS;

2. Roughness: < 2nm RMS;

3. MSF error: < 10nm / (1-5mm);

4. Processing time: < 10h/m2.

The target for this project is:

Fig. 6 Surface structure showing MSF features In 2012, Castelli scrutinised the MSF on a 400mm

diameter surface processed by plasma figuring process.

1/18mm 1/9mm

4. Previous research The largest and most sophisticated plasma

figuring machine, Helios 1200(Figure 5), was

created in 2008. Plasma figuring of a 440mm

sized substrate was performed in less than 2.5

hours achieving 30nm RMS form accuracy from

an initial 2.5 micrometre PV value (carried out

by Castelli in 2012). However, mid spatial

frequency (MSF) structure was evident. Figure

6 highlights this surface structure showing the

main spatial frequency and its harmonics.

Fig. 5 Helios 1200

5. Numerical simulation of plasma nozzle designs This paper introduces initial computational fluid dynamics (CFD) modelling of the

plasma torch nozzle designs , based in the software package FLUENT (Figure 7). The

fluid is simplified to be high temperature argon gas, and is also assumed axisymmetric,

uniform, steady and laminar.

Fig. 7 Overview of the CFD investigation 3D drawing of the plasma figuring torch (left);

2D CFD simulation illustration of flow velocity in the nozzle (right).

Precision Engineering Institute, Cranfield University, Bedford, United Kingdom

Fig.9 Curves of the etched area and gas velocity.

As shown in Figure 8 the “Pathway of Investigation” is characterised by regions

experiencing either downwards and upwards flow directions. The negative regions are

considered to be those which will experience the presence of the radical compounds.

From a processing view point, the plasma etching is considered to take place only in the

region exposed to free radicals.

Fig. 8 Vertical flow velocity plots along the pathway of investigation.

Figure 9 combines images from the gas flow

simulation model and footprint experiment

data (carried out in 2010, by Castelli). This

figure highlights correlation between the

material removal footprint and the regions

exposed to free radicals.

Fig.10 Parameters of nozzle.

Fig.11 Design parameters versus the radius exposed to free radicals (♦); Design parameters versus the maximum velocity in the throat (▲).

There are 3 general design rules of the De-Laval nozzle from the results in Figure 11:

1. Radius exposed to free radicals decreases significantly as the throat (D2) shrinks;

2. Radius exposed to free radicals decreases when the divergent end (D3) shrinks;

3. Smaller energy beam footprints should be achieved with adjustment of D2 as it is

more efficient than tuning D3.

7. Conclusions An initial 2D axis-symmetry numerical model of an existing torch nozzle has been

created. This simple model has indicated some sensible results when compared to

actual process data of removal footprints. Some initial design rules and nozzle

parameter sensitivity analysis has been obtained. This information can be used to create

a number of new nozzle designs for future experiments.

8. Future work 1. Measurement using plasma diagnostic for more accurate parameters;

2. Fluid will be argon plasma instead of hot argon pure argon;

3. Taking the turbulence and swirl into account;

4. Further validation through material removal footprint trial.

a) Effect of D2

b) Effect of D3

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Depth of the divergent path-h3 (mm) Depth of the divergent path-h3 (mm)

Diameter of the throat-D2 (mm) Diameter of the divergent end-D3 (mm)

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Flow input ( argon )

Substrate ( fused silica )

Pathway of investigation

ICP torch

De-Laval nozzle