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PHYSICS AUXILIARY PUBLICATION SERVICE

Document No: PFBPE-03-2524-42

Journal Reference: Physics of Fluids B Vol. 3, No. 9 September 1991

Title: Atomic Collision Processes in Plasma Physics Experiments

Authors: R. L. Freeman and E. M. Jones

Current Physics Microform Reference: 9109E-1765

A service of the American Institute of Physics

u UKAEA RESEARCH-GROUP

Report

A T O M I C C O L L I S I O N PROCESSES I N PLASMA PHYSICS EXPERIMENTS

Analytic expressions for selected cross-sections and Maxwellian rate coefficients

R L FREEMAN

E M JONES

C U L H A M LABORATORY Abingdon Berkshire

1974

Available from H. M. Stationery Office c:i8 PRICE £1.00

Enquiries about copyright and reproduction should be addressed to the Librarian, U K A E A , Culham Laboratory, Abingdon, Oxfordshire, England

© - UNITED KINGDOM A T O M I C ENERGY A U T H O R I T Y - 1974 Enquiries about copyright and reproduction should be addressed to the Librarian, U K A E A , Culham Laboratory, Abingdon, Oxfordshire, England

U.D.C. 533.92:539.186 539.186:533.92

Corrigendum to

CLM-R 137 (issued May, 1976)

ATOMIC COLLISION PROCESSES IN PLASMA PHYSICS EXPERIMENTS

by

R.L. Freeman, EjM. Jones

Will you please note the following corrections:-

Page 2, lines 6 & 7

2 o * v delete: v = I \ the mean-velocity of the target electron

q ll m

e / v. = velocity of an electron corresponding to the ionization

potential

insert: v^ = the velocity of the target proton

2u. v . ^ I the velocity of an electron corresponding

e to the ionization potential

Page A, section 3

delete: a

insert: In c

U.K..A.E.A. Research Group Culham Laboratory Abingdon Oxon. 0X16 3DB

September 1976

CLM-R 137

A T O M I C COLLIS ION PROCESSES IN PLASMA PHYSICS EXPERIMENTS

Analytic expressions for selected cross-sections and Maxwellian rate coefficients

R L Freeman, E H Jones.

ABSTRACT

Convenient analytic expressions have been obtained for^the cross-secticms

and the Maxwellian rajje coefficients for electron ionisation, proton ionisation,

and proton charge exchange. These expressions were obtained for atomic and

molecular hydrogen, the alkali metals, the rare gases, calcium and magnesium.

The rates for these sane processes have been evaluated for 5 _and 10 keV atomic

hydrogen be ams in atomic hydrogen.

The experimental values for the ionisation and charge exchange cross-sections

were fitted either by the analytic expressions of Gryzinski^'^ or by a polynom

ial, and these analytic expressions were then used for integration Over a

Maxwellian velocity distribution. The values of the rate coefficients were

fitted in selected cases with a polynomial and the coefficients for this polynom

ial are tabulated. Plots of the analytic fits to the experimental cross-sections

and the Maxwellian rate coefficients are given in each case.

UKAEA Research Group Culham Laboratory Abingdon Berkshire

i[aV 1 9 7 4 ^ SBN 35311 027 1

INTRODUCTION

The cross-sections and rate coefficients presented in this report have been

collected during studies of plasma diagnostic techniques using atom beams,

and from the development of zero and one-dimensional codes to follow plasma

behaviour.

Such codes require the inclusion of basic ionisation and charge transfer

processes in the form of rate coefficients. To eliminate the time consuming

process of integrating the cross-sections over a Maxwellian distribution func

tion at each time step in the code it was decided to evaluate the coefficient

as a function of energy and fit a polynomial to the resulting curve.

The analytic forms derived by Gryzinski are simple and give reasonable

agreement with the practical data for electron and proton ionisation cross-

sections, but a polynomial fit was used for the charge exchange cross-sections

because the Gryzinski expressions do not fit the experimental data.

1. GRYZINSKI EXPRESSIONS

The Gryzinski analytic form used for single ionisation by an electron was:

o - g i(x) u i

where g i(x) - 1 ( fr f ) ( 1 + f ( 1 " 2^ }- * n ( 2 ' 7 +

and x is the ratio of the kinetic energy of the bombarding electron to the

binding energy of the orbital electron (x = Ei/u^), and <J0 »• 6.56 x 10~1 ** Z 2

eV 2 cm 2 .

j The form for single ionisation by protons was

.if.

below the apparent, threshold (vq < 0.224 v^) (MB. change in threshold from (1 c)

Gryzinski ') 3 4,

? . | ( . 4 * [ ^ W t - ; c ^ < , + ' f >]

• the velocity of the target proton

2u. \ * v^ ° I — — the velocity orân electron corresponding "|

e to the ionization potential J

Both forms are summed over the number of shells to obtain the total contribution. (2)

The shell edge potentials used to describe each shell were taken from Mordberg^ ,

Slater^\ Bearden^ and Hill^ 5\ and are listed in Table 1.

2. FIT TO EXPERIMENTAL DATA OF THE GRYZINSKI ANALYTIC FORM i

2.1 Electron ionisation cross-sections

The analytic forms of the cross-sections and some experimental data are

presented in graphical form in Figs 1 to 28.

Figs 1 and 2 show theânalytic cross-sections for ionisation of atomic and

molecular hydrogen. The agreement is good in both cases, with the maximum dev

iation from the practical data being 12% for atomic and 20% for molecular

hydrogen.

For helium (Fig 3) the agreement is good at high energies (maximum error of

14% between 500 and 10**eV), but below 500 eV the error can be as large as 27%.

The agreement between the analytic form and the experimental data for neon (Fig 4')

is non-existent; at low energies the analytic form is a factor of 4 too large.

- 2 - / J

The curves for argon, krypton and xenon, show better agreement. At low

energies the argon curve (Fig 5) matches one set of data, but at high energies

it is up to 30% too low. The krypton • curve (Fig 6) is within 26% of the experi

mental results below 200 eV, but the agreement, deteriorates steadily above this

energy and the curve is 50% low at 101* eV. Xenon (Fig 7 ) shows similar defects

being within 20% at worst below 200 eV, but becoming 30% too low at 101* eV.

In the,, cases of the alkali metals (Figs 8-12) the errors in the experimen

tal data are larger, but agreement with th'e analytic form is good. For lithium

(Fig 8) the largest error is at the peak of the curve ( 27%).

At high energies the sodium experimental data (Fi^ 9) spans the curve,

while at low energies the error decreases from 60% at 7 eV to 14% at 30 eV.

The potassium data (Fig 10) shows a similar effect, though not so marked. The

rubidium curve (Fig 11) lies midway between the two sets of data at high energies,

while at low energies the error decreases from 50% at 5 eV to 10% at 10 eV.

The experimental data for caesium (Fig 12) is a good fit up to 10 eV, in

the range 10-100 eV the maximum error is 23%, but from 100 eV upwards the data

and curve fit exactly.

In the cases of magnesium and calcium the analytic form is a very bad fit.

The fit could be improved slightly by multiplying the analytic values by 2.2

for magnesium, and 1.4 for calcium.

2.2 Proton ionisation cross-sections

The Gryzinski expression for proton ionisation is a poorer fit to the prac

tical data than the electron ionisation model.

The hydrogen, helium and neon data, shown in Figs 15-18 have polynomial

fits (dashed curve) as well as the Gryzinski curves (solid line). The polynom

ial fitting procedure will be discussed in the next section.

In the cases of atomic hydrogen (Fig 15) the Gryzinski curve and data match

above 2 x 10'*eV (maximum-error 10%), but at low energies the analytic form

- 6

drops, off too slowly; Similarly, for molecular hydrogen <Fig 1.6) the-.fit- is

good above 5 x 101*eV but below this level the curve exceeds the data by some

50% at lOêV, and the curve then drops away too quickly. Helium (Fig 17) shows

the same behaviour as molecular hydrogen, while the neon data and curve again

bear no relation to each other.

Both argon and krypton show some 30% deviation from the practical data,

and no experimental data has been collected for the remaining curves.

3. POLYNOMIAL FITS

In cases of special interest for the computer codes the agreement between

practical data and the Gryzinski analytic form for- proton ionisation could be

improved.

In these cases (H, H 2 and H e) a polynomial of the form n

* imo

was fitted to the practical data and is plotted on the graphs (Figs 15-17) as

a dashed curve. The same form of polynomial was used to fit the charge exchange

data.

4. CHARGE EXCHANGE

The Gryzinski analytic form for charge exchange cross-sections is extremely

poor when compared to the practical data. To have some expression for this

cross-section a polynomial of the form previously mentioned was fitted to the

practical data.

In the cases of molecular hydrogen, krypton, xenon and magnesium, the odd

points below the maxima at the low energy side were assumed to indicate that

the cross-section had passed its maximum and would decrease. The curves have,

been fitted accordingly.

The coefficients of the polynomial fits for the proton ionisation and the

charge exchange cross-sections are listed in Table 2, along with their ranges of

validity. _ A _rj

-5. . ' RATE COEFFICIENTS

- 5 - $

Rate coefficients o.v (cross-sections at a given energy multiplied

by electron or proton velocity at the same energy) and rate coefficients eval

uated over a Maxwellian velocity distribution <a.v> have been evaluated for

all three processes. In the cases where a polynomial fit has been obtained

for the cross-section this was used in preference to the Gryzinski form in the

integration routines, and the results are shown graphically in Figs 37-50.

For the Maxwellian rate coefficients the energy scale gives the temperature

of the Maxwellian distribution. The resulting rate coefficients for several

cases have been fitted with polynomials and the coefficients and ranges of

validity are given in Table 3.

6. IONISATION OF ENERGETIC ATOMIC BEAMS

Maxwellian rate coefficients for ionisation by electrons and ionisation •

and charge exchange of protons with energetic atomic hydrogen beams of energy

5 keV and 10 keV have been evaluated. Polynomials have been fitted to the curves,

and the coefficients and ranges of validity are given in Table 4.

, The curves are shown in Figs 51-53, and are'of particular interest in the

study of neutral injection in the levitron.

SUMMARY

It can be seen that the Gryzinski form for both electron and proton ioni

sation gives a useful estimate of the cross-sections (with the exception of

neon). If a more accurate value is needed a polynomial fit is necessary.

No attempt has been made in this note to give comprehensive data for the

cases considered, or to judge the accuracy of the experimental data.

Electron Ionisation Cross-sections

10-'

5 J 2 a $

ir/1

» Cowling » Fletcher (FUPH-A-63) o Rapp 46<*len(JJChf»i)»iys. 43-1965) • Sdrim EtoXPtiydeo 31-1965) o*Schrom EtoJ (Ftysieo 32-1966) Ionisation curves from foraula of Gryzinski (Atomic collision processes

London eonf. 1963)


London eonf. 1963)


London eonf. 1963) j


London eonf. 1963)

/ - M

/ c < >

< 1 *

<

\ e i

1 e i r \ * ]

Hk."- \

s • i

i \

. ,! i

10 10' »5

Electron energy (eV)

10'

Fig.2 Ionisation of molecular hydrogen by electrons

1

Electron Ionisation Cross-sections Continued

10-"

E

S

icr"

icr"

• - -

•i +

• < •i +

• <

•s. •

•s.

1 1 7

E „ • r lm»r i n t i

• •

• Schram et al/Physica 31-1965 iPhyslca 32-1966

•Kieffer Rev. Mod. Phys. 38-1966

Theoretical curve Gryzinski (Atomic collision processes London conf I 9 W ) *

I I I f i l l ' 1 1

I • Schram et al/Physica 31-1965

iPhyslca 32-1966 •Kieffer Rev. Mod. Phys. 38-1966


I I I f i l l ' 1 1




I I I f i l l ' 1 1




I I I f i l l ' 1 1

1




I I I f i l l ' 1 1




I I I f i l l ' 1 1 ' ! i

10 I0 2 , I0 3

Electron energy (eV) ^

Fig.3 Ionisation of helium by electrons

(04

Electron energy (eV) Fig.4 Ionisation of neon by electrons

/o


e o

w3


Fig.5 Ionisation of argon by electrons

icr'5

10'

S

o

IO" 1 7

10' rl8

"Experimental points _-Schram et aljPhysica

.Physica 32H966 * Rapp i Golden J. Ch

r Theoretical curve Gryzinski (Atomic

(-collision processes London conf. 1963)

10 IO 2 . IO5


Fig.6 Ionisation of krypton by electrons

IO 4 IO5



Eltctron tnergy (tV)

Fig.8 Ionisation of lithium by electrons

10*

Eltetrtn tntrgy (tV)

Fig.9 Ionisation of sodium by electrons

Electron lonisation Cross-sections Continued

Electron cntrgy (tV)

Fig. 10 lonisation of potassium by electrons

Eitctron tntrgy (tV)

Fig.11 lonisation of rubidium by electrons


| Thtorctical curves fro* forault of Cryzlnski (Atonic collision proctuos London eonf . 1963)

Experimental points i Zapesectoyl U.E.T.P. 28-1969) • Kitfftr«tv.Mod.Pbyt 36-1966) • MeForlond • IHnney (Phys. lev 137-1965)

! Thtorctical curves fro* forault of Cryzlnski (Atonic collision proctuos London eonf . 1963)


Thtorctical curves fro* forault of Cryzlnski (Atonic collision proctuos London eonf . 1963)






A N ygocrd (J.Chet». Phys. 49-1968) o Korchcvoi i Przonski • \ .. UE.T P24 1967).

ygocrd (J.Chet». Phys. 49-1968) o Korchcvoi i Przonski • \ .. UE.T P24 1967). W ygocrd (J.Chet». Phys. 49-1968) o Korchcvoi i Przonski • \ .. UE.T P24 1967).

i / 1 i—

J X f. t

•

/

N •

^ • J J ^ / ! i y \

10 10* * I0 1 to4

Eltctron tntrgy (tV>

Fig. 12 Ionisation of caesium by electrons

J5

Electron lonisation Cross-sections Continued

1 1

1

•

. e

v 4 o.

>

- 1

t *

Theoretical eurvts from formula of firyzinski (AtoMle collision processes London conf. 1963) 0 Okunu ct al. (J.Phyv soc Japan 29-1970

1 1 I 1 1 1 1 -

Theoretical eurvts from formula of firyzinski (AtoMle collision processes London conf. 1963) 0 Okunu ct al. (J.Phyv soc Japan 29-1970

1 1 I 1 1 1 1 lo 10* I0 1 I0 4

Eitctron tntrgy (*'V)

Fig.13 lonisation of magnesium by electrons

Experimental points + McFarland ( Phy s. Rev. I59,20-1967 )

I 10 10* I0 3 I 0 4

Electron energy ( eV )

Fig.14 lonisation of calcium by electrons

Proton lonisation Cross-tactiom

Proton energy (eV)

Fig. 15 lonisation of atomic hydrogen by protons

I0 ' 1

10"

l 0 - i«i

*.Gordwv» Pnncv (J.T.P. 9-1964) « HollriehtrfZ Phys 167-1965) • D» Httrttol (Physica 32-19667 • Solovev (JI.T.R 15-1962) o Fogd(J£.T.R 1-1955) a Mc Daniel Etal (Phys. R«v. 121-1961) * AfrosJ«ov(J.E.T.P. 7-1958)

Curve, f i t to proctlcol data Sryxiniki



1 i



-1

i i


Curve, f i t to proctlcol data Sryxiniki t

•

•



*

• " 1 1 i * •

/ S

/ s I |

! \

—" • * 7 Sf

A / / /

/ I

i

i

I i 1 ! 1

i * ^ i

A . ' ' •

s

i : i i i i

N \

f I ! I

1 ! i !

1 1 ! 1 1

1 1 1 i :

! 1 ' i

• !

• K i

! I 1

/ 1

!

! i i i

1 1 | i i 1

i : 1 ! : !

. i ! 1 !

' 1 • i ;

i ' ! !

Proton energy (eV)

Fig.16 lonisation of molecular hydrogen by protons

11

Proton Ionisation Cross-sections Continued


1 I ' -I I ! I I I i

c . I

! 1 • T

I

\ J V % t

! i

i 1 i

i ! i

•

R • .

— — •

h Thtorctical curves fro« formula of Gryzinski (ATOMIE collision proctssts London conf. 1963) Expcrimtntal points

• i \

/ Thtorctical curves fro« formula of Gryzinski (ATOMIE collision proctssts London conf. 1963) Expcrimtntal points

/ > MeOanitl «T al(5th Proc Ion. Phtnosu In fasts nunicn ivoii

/ +DcHttr t t al (Physlea 32-1966)

/ 1 ' I \

- — 1 ' I \

- —

1 - k I

I

1 i > > .

, i X I

Proton tn t r j y (tV)

Fig.19 Ionisation of argonV/ protons

10' . I 0 5 10* I0 7

Proton tntrgy (tV )

Fig.20 Ionisation of krypton by protons

Proton lonisation Cross-sections Continued

F.ig.21 lonisation of xenon by protons


10"

10

1 1 i 1 ! i 1 1 I I . ! 1 I ! !' • Theoretical curves f ro* formula of Cryzinskl (Atonic collltien processes i . i - _ a i a i i ^

1 1

• i Theoretical curves f ro* formula of

Cryzinskl (Atonic collltien processes i . i - _ a i a i i ^

1 1 i

-k i n u v u c v i h . i t \ j j

1 i 1 i

3 1 1

1 1 , i I I 1 i

! |

I ' 1 i I I

1

—- J • J ,

i 1 i —- J

i 1 1

1 I i

i i , . i ! |

; !

i ! 1

1 ! ; 1 ' j 1 i

1 \ " " 1 • i 1 i !

|

i 1

1 I I I i I I I I I • I I M I ! I \ \ I I ijp • 1 0 * I 0 5 10* 10

Proton energy (eV)

Fig.22 lonisation of lithium by protons

Theoretical curves from ferula of Cryzinskl (Atomic collision processes London conf. 1963)

I 0 5 10* I 0 5 IO ' I 0 7

Proton .energy (cV)

Fig.23 lonisation of potassium by protons


1 1 1 1 1 1 1

Thtorctical curves from formula of -Sryzinski (Atomic collision proetssts -Thtorctical curves from formula of -Sryzinski (Atomic collision proetssts -L onaon com. iio

i

1

-

j j i I I

— / i i — / 1 l

I

' 1 1 1

X .

^ O / t v . . \ w

1 • 1 v.

i i

1 \ 1 »—a • *—I. — I — -I I , . 1 1— —I 1 1—- I 1 . 1 1 - __J 1 3l .1 I 10 KT 10 10-* I07

Proton energy (tV)

Fig.24 Ionisation of sodium by protons

1 ' > • ; • 1 ! 1 ! 1 1 I • • 1 i Th»i>f»»ifiii rwr u t t from formula of I

! i • i i !Cryzihski (Atomic collision processes i 1 1 i

j

1 j

| i I I i i ' I i

onaon com. ivojj ! i ; • ! : i i 1 * 1

1 1

1 i I

! 1

1 ! I 1 I

S 1 | \ i ! \ . ; | | / : 1 | — ' ' " r V , ^ X i l i 1 ! |

/ 1 -1 i i ! V . X ! 1 1

1: 1 i / 1

1 ! ' i i !

N X

. 1 !

i / • # 1 1

! i i X .

\ X . 1

/ 1 i \ ' < / • ' • • i . ; >

1 \ X X

i 1

1 1 1

/ 1 ; ; i

I- ! ! 1

/ I 1

-i / '• ' X i io3

10* io! 10* io7

Proton energy (tV )

Fig.25 Ionisation of rubidium by protons

Proton lonisation Crow-sections Continued

Proton energy (tV )

Fig.26 lonisation of caesium by protons

J3


- I - 1 1 1 1 1 1 I I I T h e n a r * f t f e a l e u r v c i f rOB forsula of Cryzinskl (Atomic collision proctssts .London eonf. 1963) 1 < —

i i : i

- ; i i i

-

-

I 6

I • I I I I I I • ! ! 1_4 1 1 1 — J — I — 1 1 1 ••—> | 0 J I0 3 I 0 4 I 0 5 I0 6

Proton energy (eV)

Fig.27 lonisation of magnesium by protons

Theoretical curves from formula of Cryzinski (Atomic collision processes London eonf. 1963)

Proton energy (tV)

Fig.28 lonisation of calcium by protons

Charge Exchange Cross-sections

10"p

10

10

J I —1 i

•

i

i :

afiardeov l f J TP 0 - 1 0 4 * 1 •

- • Fit* 4 St«bblnis(rtiys.«J*l*W^60* ) nit

• 1 • i

— * n

• «B« t * s Br ilyoav

•ek it a

• 01 ) ( rt

Phys.R h int.e

•v 112-mf. al*

958 ctre

) nit : i aUMie coll. Li tnin jra d 967) !

_ _ l l w l » r » f N u e U a r fu * i«n 11-1971)

-— t

*\

• • 4

*\

Proton antra,? (tV)

Fig.29 Charge exchange cross-section protons on atomic hydrogen

» Gord«tviPaMv(J.T.P-9-l964)| x StodfardsHcsttdtPrtcltySoc.

A227-I955) • 0* Httr del (Physic* 32-1966) o Fo«*l*tal(J.E.T.P 1-1955) • Rib* rtoMPhys.Rey.83-1951)

— Curve fit U •radical data 9 KoopawnCPhyvRiv 154-1967)

K)' I04

Protoo energy (tV)

Fig.30 Charge exchange cross-section for molecular hydrogen ( H + + H : -* ftj + H)

http://rtoMPhys.Rey.83-

Charge Exchange Cross-sections Continued itinunu / jj

o1 I03

• D«H«tr(rTr/siea 32-1964) x Stcdcfe^*He|ttd(»hvs.lloy.Soc.

A227-I954> • Stitr i Be/nttt (Phys.lUv. 103-

I9S6) Ptlyneaiol f i t

10' to Proton entity (tV)

Fig.31 Charge exchange cross-section for helium

•l . i 1

- L U

•A—i—i i . i -T I T

! 1 i; !

• » 7

i ! 1 i - i i 1 — 1—i j . • ! ; iii Dc H « r (Phy»ica 72 -T9«> f

' ! ! : 1 !

' 1 I" \ r • St*r«td(Phy».Krvl03-195n

• London A227-S5S Pa ly i ta in f i t

! • i 1 ; ; i 1 i ;

1 x — • • 1 I ;

i ' i • • ! i

/ ! i

; 1 V 1

• ' t

j 1 . ' /

/*

:

i i | -

!

1 j

. / I L

1 1 1 •

to'

10

10 I 0 - 1 0 "

P r o t o n tntrgy (cV) 1 0 -

Fig.32 Charge exchange cross-section for neon

Charge Exchange Crosi-jections Continued

10

10

_ + Sti*r » Bernttt (Phys ft** 103-1956) .[>* Heeret *l (Phytic* 32-1966) >St««-*f*ri- tt * l (Pr«c R*y,S*c A227-I955)( * D * n n * t * l (Phys Rev 154-1967)

P*ly«o«l*l f i t

10 10 10

Prtttn energy (tV)

Fig.33 Charge exchange cr&ss-jection for argon

10*

¥ De H < « r el a l (Physjca 32 -1966) Stedeford & Hasted (ProcRoy.SocA227-1955) Tuburen el al (Phys.Rev 171 -1968) Afrosimov et ol(2T*ch Ft* 3 0 - 1 9 6 0 1

m

De H < « r el a l (Physjca 32 -1966) Stedeford & Hasted (ProcRoy.SocA227-1955) Tuburen el al (Phys.Rev 171 -1968) Afrosimov et ol(2T*ch Ft* 3 0 - 1 9 6 0 1

X A

De H < « r el a l (Physjca 32 -1966) Stedeford & Hasted (ProcRoy.SocA227-1955) Tuburen el al (Phys.Rev 171 -1968) Afrosimov et ol(2T*ch Ft* 3 0 - 1 9 6 0 1 Polynomial curve fi

• / ^ ^ ^ ^

/ /

\

! 1 i 1

: / • • — - f — — - \

- \ *

i i 7\_ | i

i \ 10J » 3 W 4 * XD5 10?

Proton energy (eV)

Fig.34 Charge exchange crost-jection for4tryplon

Charge Exchange Cross-sections Continued

• »

ct fll (Phys. R«v. 154- 1967) L • Durr ct fll (Phys. R«v. 154- 1967) L • ••

» x SUdettrd & HasUd (Proc Roy Soc *J 27-1 95! >)

• - +x-:

—*- F tlyeati la!

\

V i 1

4 • / K i • r \ •

\ |

\ r ^

•

\ ' 1

• 1 - 1

1 i i

'. 1 ! i

, 1. 1 i . \ , i ,

HI

10 10* B 5 I0 4

Praton antrjy (tV)

Fig.35 Charge exchange cross-section for xenon

10J 10"

1 0 ' P r o t o n c n « r g y ( tV)

Fig.36 Charge exchange cross-section for magnesium

Rate Coefficients for Electron and Proton lonisation and Charqe-Exchange

Rate Coefficients for Electron and Proton Ionisation and Charge Exchange Continued

Rate Coefficients for Electron and Proton lonisation and Charge Exchange Continued

Particli energy (tV)

Fig.42 Rate coefficients for krypton

31


Rate Coefficient! for Electron and Proton Ionisation and Charge Exchange Continued

10 1 1

i I 1 i r .

• i i •

i — _. Proton lonl •at Ion av.- \ Electro* Ionisation

i 1 L

v i

! 1 j \ . i . : i

i • . i 1 i i

/ / " I '

1 i j /

10 10 I 10 10 4 10 $ 10* Particle energy ( eV )

Fig.44 Rate coefficients for lithium

r

i

— 1 i ! ' ; 1 1 i 1

1 — - - ! ! . I i 1 I | • oton Ionisation

_^ 1 — - -

i I * i 1 I | • oton Ionisation

* y

— i

1 X * y

— 1 X *

y j i 1

^^ss>^0 / ' <orv>

. 1 1 — 1

1 i i / / \ OM. i | 1 / / 1 ' ;' ! i

\ j

/ ; 1 1 ; 1

1 : ! ' 1 j <c v> / i i 7 !

\ j

i i ,

'i 1 ' '••

\ |

i

10 I0 J I0 3 IO4 I 0 5 10s

Particle energy (tV )

Fig.45 Rate coefficients for potassium

3 3


Iff'

3 • 10

irj

1 l ! 1 ! 1 | 1 • I 1 i 1 r | 1 i

! I 1 i • I i i

Elec tre n lonisation I ( j I j Proton lonisation

• *^3aT" IV. 1 y S/ /

i • ! i 1 | ! j

y S/ / 1 i ' ! i

1 ;

1 '• i i / / 1 i : ! 1 ' 1 ! 1 j / /

/ /

i ! i

/ / / / •"—c.v.

— < C V>

i I 1

i 1/

' 1 /

/ I / I

1 1

10 10' I0 J I0 4 I0 J

Particle energy (eV )

Fig.46 Rate coefficients for sodium

10

10 =

i - ! 1 1 1 i • ! I : i r " ton lonisation 1 1 1

• 1 1 ! r r g : i r " ton lonisation 1 1

c i v c i r D f i i a n i > H i i w n • • — 1

P T ^ i i • 1 Y\ \

• !

^ « w . | • ; , i \ 1 , i i \ ; / /

/ / 1 r 1 s

i ; 1 :. i i i ~ / [ / I ! i l ; i ; ! i i i

\ i ! / f\ j 1 I

! : l i 1 / / / - • ! I ; j

1 . i ; i ! ; 1 i

;

— /

/

1 !

i • 1

1 . « 7 V > /

y

— /

/

1 ! x « i j | ;

i 1

j 1

10 - 7

10' 10 10' I0 J I04 io-Partlcle energy { eV )

Fig.47 Rate coefficients for caesium

10*


1 | 1 I 1 I < |

Eltctron ionisation i i - — — = = j ~ a . ^

r — <o- .v .>

1

* *

——— it 1

i / ' \ ' 1 •v. i 1

| / I / ! i 1 1 j

1 / / i I

1 / / I :

i 1 1 — — i —

< a V j

. i I /

I 1 1

1 .1

j 1 i l

I i 1 / 1 / I 1 • i i .; i - i i i [ i i i i . i i

IO2 IO3 10* IO5 10' Particle tntrgy ( tV) ~~

Fig.48 Rate coefficients for rubidium

3.5


•article energy (eV)

Fig.49 Rate coefficients for magnesium

3<f

Energetic Hydrogen Atom Rate Coefficients


Fig.51 Maxwellian rate coefficient for electron ionisation of energetic hydrogen atoms

1 — I - • 4 -

— i — 1 - r

1 1 1 1 — :

• 1 1 1 r - i -_ i U - | > i i

p.H(5K«V) p.H(K)KeV) I — j . i 1 1 ! ; ! 1 : 1

1 1

p.H(5K«V) p.H(K)KeV)

I I ! i

i

! !

1 ; 1 1 ; i

• i

: r 1 i

1 1 ! I

7 i i i i i

i \ j ! • T i

1 i 1 i i 1 i j

I 1 ! ! i 1

I i ' 1 i l , 1 i 1 j i 1 1 I ' 1 I • — L — I ' — r - r 1 ! •

i I 1 ' i i

• i i ; 1 ' i | - r

i i i

1 • — • —

i 1 ' i 1

' i i ! 1 1 — 1 — f _

: i i 1

1 1

* i. 1 1 1 '

~~ s

' ! ! 1 '

— — h i : ' ' 1 1 L ] '

1 1 • y ' ' ' T - : : 1

i . ! j 1

i 1 i ; : ' . ;

i 1 1 i 1 — ' , i

i i i i 1 i i i • ' 1

! | 1 i I I I

I i • ' !

; : . i •'. —.—, • i ! ——.—4—

i i

j i i i 1 i

i • 1

i . ; , 1 I I I

1 , 1 i - 1 ;

• I

1 1 ', ' 1 i I ' ' L- ! 1 — i - l 1 i L _ U I i : 1 I i i I i j • ' I

» 0 to1 io1 io1 io1 io1 io6

Proton energy («V)

Fig.52 Maxwelliin rate coefficient for proton ionisation of energetic hydrogen atoms

3 1

Energetic Hydrogen Atom Rate Coefficients Continued

| i 1 1 i

pvH(5K*V) p.H(K)K*V)

1 I ] ! , 1

i 1 i , 1 i i I

pvH(5K*V) p.H(K)K*V) : 1 i : i 1 1 i

pvH(5K*V) p.H(K)K*V)

i i • l

1 ! !

1 1 ' ' i ' 1 ;

! ! i i !

1 i i 1 1 1 i i i l l 1 i l l ' i • 1 i '. 1 1

i | 1 ! 1 ' 1 • 1 1 i V 1 .

1

i 1 ! ! 1 1 l i

; i . , i

i 1 i :

i ; i : 1 1

i 1 •

!

j i

i j : ;

1 . i 1 i

i • i . . i . \ — 1 (—1— i : ; • \ ! ' ! -; ; i 1 \ ! • !

--! \ i'

1

-- 1 \ 1 '

1 | 1 i , :

1 \ ! i i i ; ; | '

! ! 1 i

1 i 1 1

' ! i i ! i i 1 : l 1

• i I i ;

1 i ! i I ! i I I I ; I i . I , 1 : ! l_ I _J , . i l l . 1 i i_LJ . 107J JO5 102 » 3 K34 X) 5 » 9

Proton energy(eV)

Fig.53 Maxwellian rate coefficient for charge exchange of protons on energetic hydrogen atoms

32 I C F Review

In addition, experiments with disk* have demonstrated or inferred that x-ray conversion efficiency (at a given wavelength, platma composition and intensity) increases with pulse length, spot size, and potentially beam quality. White our prevent modeling can match much of the data, some of the trends seen in the data (i.e., spot size dependence) are not quantitatively understood.

X - ray conversion experiments planned over the next several years will further build upon our extensive data base and attempt to develop an improved modeling capability. Experiments will focus on areas of applicability to the NOVA Upgrade. The power and energy capabilities of NOVA will limit the overall parameter range that can be experimentally addressed.

The goals and objectives for H L P 7 are:

Since the required conversion efficiency, », (more importantly nl) has been already achieved and the favorable trends in conversion efficiency as a function of tho parameters associated with the NOVA Upgrade (compared to NOVA) have also been observed, we feel no additional miles tones are required. The experiments will be used primarily to improve our understanding of the appropriate physics so that we will he able to better predict the range of hohlraum performance that will be available on the Upgrade.

Capsule Physics ( H E P )

An extensive program addressing the implosion physics of ignition and gain is presently underway on NOVA. The goal of this effort is to further develop and demonstrate a quantitative and predictive understanding of the performance of capsules (properly scaled from ignition/gain designs) including the effects of hydrodynamic instability and x-ray drive non-uniformities (with known initial fabrication tolerances of the target and a detailed knowledge of the hohlraum environment). The extensive diagnostics utilized in the H E P Program also allows confirmation of our ability to model ignition physics in imploding capsules, i.e., the balance between PdV work and electron conduction and radiative losses in (he fuel in the absence of alpha heating.

The H E P experiments utilize both planar targets and capsules with/without prescribed perturbations (incspsule fabrication or x-ray flux uniformity). The targets do not include cryogenic fuel configurations. The experiments are extensively diagnosed with x-ray and neutron diagnostics including x-ray backlighting. The experiments also emphasize pulse shaped drive to enable minimum entropy implosion trajectories to be examined.

Although not one of the principal objectives of the H E P Program, the pulse shaping and the reduced levels of preheat from high energy photons and superthermal electrons lead to non-cryogenic implosions with final fuel densities in the range of 40 g/cm 1. The specific goals/objectives of H E P are the following:

(HF.PI) Demonstration of increased fuel/pusher compressions with high contrast pulse shaping with noncryogenic targets. These experiments have been successfully conducted but due to the high compressions achieved, limited diagnostics were

TABLE 2

CROSS-SECTION r i a c t i o n A , Ai A i « l A . A | A , N

HANOI ' (•V)

UNITS ol itr*)'

mOTCM IONIIATION

» • M 44303300a IO 1 o j u m i i i o ' 4104(1»4a lo ' o j i 39339 -0.744447S.101 04480113110'' 4J400444.10'* 100 —(alO* kiV » • M, 4J07e03(>10 3 o.iii7oo7aio' -aw*o«oi 0-3470(39 4 * 3 ( 4 3 9 ( > 1 0 ' ' 0 .101 T304al0''

flJtaOTO.10"' 100 -IO' k4V

( • M. 4.4079443a IO 1

aiSM3(]>101 44003730 0.0443471 4.1430087 01(00330.10' ' 44330*41alO' ' 100-MO* u v

» • * • " 4.4134772«I0 J 0.174444(,10' 4J780742 O.S2J(ai7 4-239*300 o.motTO.io'1 44471»30»10 ' ' 0346143tal0 ' 4.9343443al0"' i a > - i o ' a«V

CHAAQ1 IXCHANSf 04037 « 1 0 1 4

11 •O.lMIOf, , ! ! 1 o n 1 1 — 10* • V 1 • 0.1112 « io ' 1 4 t ' J

• V

4 . IOM170a l0 1 O-SeWJla tO 1 : a i H i n o i i o 1 4-3301031al0' 0.3312*37 4.1000713110' 1 0J439434 .10 ' 1 JO-Sa lO* aV

P«-Ha AaaMOWxIO* 0-23010C4.101 -a i ' imoa ia 1 O.1311O7I.I01 44aimi OAOUtOOalO'1 4313074O.10 ' 1 0 - 1 0 * a*V p N* -0.7002900410* 0 J M 0 T M . 1 0 J 4.1(484JTalO 1 ( L M I O M t / l O 1 43074444a io' 0J3394O3.10' 1 •amTtituio'1 10 — 1 0 * •V

P* A 4.4101 HOilO* OÎJIMOalO 1 -amTTX.itr ' aoooonaio 1

4J*74027b1o'

04000014 4 . 5 2 1 1 7 9 9 . 1 0 " ' 0.17027S4.10'' 4 3 5 5 2 4 0 1 . I O 4 1 - 1 0 ' tV p • Ki 0L22M1MI1O 1 •aosMiJJ.io' 0 J t 4 U 7 O i l O > - i lOtOHAalO 1 0.3«n7JO*a1o' 4 3403141 O331407(a10'' 447444e*al0'' 0.1403000a 1 0 " JO — 1 0 1 tV » • X* ^.xeottoiio' OJMITMjiIO1 4J0771(7a1o' 0-793(007alo' 4.1(01107i10* 03041319 4.147403*a10'' 04877004alD'' 44734334.10'* 1 - 1 0 * • V • • M , 4 .3 ( l0777aI0 1 0.3999107110' <uom40.io' 0.4331 K7a10' 4 3 7 5 * 3 3 9 . 1 0 ' 04010420 4J07( iee. io ' 1 1 0 0 - 1 0 * aav

a

TABU 3

MAXWELLIAN RATE COEFFICIENTS

I.

RIACTION A. ' ' J A] A] A. * • A. 4 . 1

*• RANG!

lavl UNITS

iCMitATiON ; 0 - M 4.1440M1XI0 1 O-TSmSTJalO1 4.33093(1alo' 0 J » 0 0 7 0 » a l 0 1 444021(4 0J309047a10 1 -0.1493409al0' 1 0 . 4 0 Q 4 1 8 1 . I O - * O.500O777. IO* 1 0 0 - 1 0 ' aV p i Hi •aSOUOTMalO' 4 .7S73( (3 i to ' OI724947.10 1 07492077 4.7071952al0"' 0.302781 7al0 1 -O.IIOTtOOalO'' 0.1379300a 10"* 100 —io' aV p . Ha 0.S737tO4«10' -0400S*SSilo' O.aatOKO.lCr1 4 . 1 3 7 3 0 4 4.10 1 0.1t0447Ial0' 4.17144234 0 9441473a IO' 1 O3n3O83a10 ' 0JS4O439a!0'' 1 0 0 - 1 0 ' aV a • M 4.3I73S40110 1 aiMsaiiaio1 4-3j33094alo' o . 7 o i i » u 4 74314*4.10 ' 04l53744al0 J ojimi7.io'1 1 - 1 0 1 aV

a * rtj •03300771a IO 1 oimsiiio 1 4.4050711.to' 0.7330010 <0.7M*3O4i10' 0 . 4 1 4 1 4 4 5 . 1 0 ' 4 4 4 3 7 1 ( ( a l 0 ' 4 1 - 1 0 * aV

a • H# 4.44(0(17alO J 03443904a IO 1 4-t02«714a10 1 O.247O931al0' 4-342*3*2 03504100.10 ' ' 4 .J43447S.10' 1 2 8 - 1 0 * aV

CHARGI IXCHANGI

p • H 4 . i ( 4 i7S7a io 1 0.829795 4.2200477 04750192al0 ' 0. 1 7 4 9 1 ( 3 .10"' 0 . 4944790 .10 0.3174410.10 ' OJiJOJOOalO"* OJTSOTtlalO -* 1 - 1 0 * aV P * Hj O43*3043a1o' -0.4473t7.alO 1 0 7 W M 1 8 . I 0 1

4.0924134.10' 0.100«433i10' 4.1040904 0 - 4 3 3 9 3 K.1O ' « 2 0 1 1 » 3 » a l O ' J 0^78*444,10' ' 1 0 — 1 0 * av

p * Ma 4504*074alO J O-347970Oalo' 4 . 9 ( t 7 9 3 1 > 1 0 ' 0.14«3333a l0 ' 41114394a10'' 0.2343324.10'' 0.314979lalO'' O.!Sl i7Otal0' ' 0^909037810^ 1 0 0 - 1 0 * . aV

T A B L E 4

MAXWELLIAN RATE COEFFICIENTS FOR BEAMS IN ATOMIC H Y D R O G E N IS kaV • 10 kaVI

fl iACTION A . *1 A, * * * 1 RAN CI UNIT* of 'SnD'

ICMItATION

p • H (9 a«V) •0.7813477.IO1 0J*S4 l l ta l0 ' O0144032 0-394Ct99a10 ' 0J5O7590.10 ' 4.102t(73al0 1 0.3113*71.10"* 1 #V -40«V - 2 SS* 10"* -IO tV — 10* «V •V . . H 19 kaVI •a7554317aIO3 0.5393130.10' O.140O947.101 0 3370800 -0.2084(09.10 1 0.IO4O474al0'1 4 217(7(9.10'" I «V — 10* tV •> • V P * H 110 k.VI ^ 1940001.IO1 0.7023243 e^55t5«3 O90l90S1a10' ai308041al0' ' -0 9317193a IO' 1 0 2214(43.10"* 1 »V —100»V • » 7-9•IO"' 100»V — 10* «V • V

a * H l lOhavl -0.23941403 10' 0 370M2I.10' 4.7190771 0.9109599.10 1 -0(202309.10 ' 0 4 3 M O U . 1 0 1 4.1002732.I0' 4 1 tV IO 1 oV • V

CHARGEIXCHANGI \

p * H 18 aaVI O.tSOSMI. 'O 1 0.9OM215.I0' 1 4.58190M.10 1 4.1703341.10 1 0.4(138»7a10'1 -0 4474339a 10 ' 0 12 t *»2 .10" 1 «V -S4101 «V • I.JW-IO'' tV 5« IO1 tV - 10* «V

p • H 1*0 aaVI 0.1504080.IO1 0.:8«21IIal0" 0.237I704.IO'' O 2012109.10 1 04C93419.I0' 4.4003(00.10 1 0.112:/25.;0"* 1 av — 1 • l»y aV ccnai - 1 10^ • V t a I0 J av — 10* aV l

http://-0.744447S.101

http://-0.4473t7.alO1

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Afrosimov V.V. , Il'in R.N. and Solovyev E.S. Z.Tech.Fiz. 3J2, 66.1 (1960).

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