High Resolution X-ray Spectroscopy Of Plasma Focus: Equipment, Modeling Of

High resolution X-ray spectroscopy of plasma focus: equipment, modeling of results E.O.Baronova, V.V.Vikhrev, M.M.Stepanenko, A.M.Stepanenko RRC Kurchatov Institute, 123182, Moscow, Russia

WHY TO MEASURE LINE EMISSION 1. Characterization of the source for different applications, including nuclear fusion, lithography, etc. 2. Plasma diagnostics : to estimate plasma size, temperature, density, distribution of ionization stages, electron beam energy, ion beam energy, strength and direction of electromagnetic fields, etc.

HOW TO MEASURE LINE EMISSION In reflection, E<10 keV

In transmission, E>8 keV A1 

Flat crystal K

Convex crystal De Broglie scheme



A2

 

2R B2 B1 A

K

(a) E  O  D

Concave crystal A

2R

(a)

B2 Johan scheme R

B1

Concave crystal Cauchois-Johann scheme

X-ray spectrometers

L<2m W=30 kg

L=0.5 m W=8 kg

Large spectrometer with 2 channels

L=0.5 m W=10 kg

Compact for Тi measurements

L<0.3 m W=1 kg

UV,EUV, X-Ray spectrometer

Supercompact Cauchois for Hard X-rays, E>8 keV

COMPACT AND SUPER COMPACT DE BROGLIE X-RAY SPECTROMETERS 1. 3crystal de Broglie spec. equipped by MCP, will be reported on July 3d. 110 mm

30 mm

2.

50mm

Spectrometer for EUV, visible and X-Ray emission

Hitachi Co grating

MCP

Gratings for EUV and visible, Bragg crystals for soft and hard Xrays. №1,  = 21°- 60°, G=2400gr/mm,

Holografic grating

Капилляр для калибровки, Capillary юстировки, литографии

№2,   =11°- 20°, G=4200 gr/mm

Optical scheme of spectrometer

Transmission regime of operation-crystals

Reflection regime of operation-crystals, gratings

Cauchois -Johansson crystal works in both transmission and reflection 1.5-400 keV - total energy range10(-1)0 cut works in reflection,energy range 1.5-13.2 keV,

11(-2)0 and 0001 cuts work in transmission, 10-400 keV

Dispersive elements: gratings for EUV & UV, crystals for X-rays Small crystals for microscopy

High refl graphite

• Large spherical crystals • CauchoisJohansson crystal • Spherical grating, Hitachi Co • Johansson spherical crystal on optical contact

Spectral resolution of device in various regimes Reflection regime (/) total = 1.7 *10-4 Transmission regime

(/) 14(-5)0 = 4* 10-4 Cu, first order of reflection (/) 13(-4)0 = 1.7* 10-3 Mo, first order of reflection (/) 20(-2)0 = 5*10-3 Mo, second order of reflection

Hot spots in plasma focus, filled by Ar number of hot spots in one shot 1-10

ArXVII spectra, single shot, many hot spots

Modeling of ArXVII in dense plasma, I=500 kA

Te = 900 eV, Ne = 8*1019 cm-3

Spectra from each hot spot

Plasma image in X-rays

X-ray spectra

Parameters of hot spots are distributed chaotically

Line emission properties • Anisotropic • Time-dependent • Inhomogeneous in space • Polarized

To create a model, which describes dynamics of plasma parameters

Requirements to the model 1. Should describe phenomena adequately 2. Should be simple 3. Should use small computer time 4. Possibility to compare with experimental results

Structure of the Model

Plasma dynamics in Z-pinch neck, model was created by Pr. V.Vikhrev in 1976, Kurchatov Institute Plasma electron temperature T is determined by Bennet equation:

I2 T 2 4c N

I – discharge current, N - number of particles in the unit pinch length in the neck

Plasma outflow from the neck:

dN N  dt 

 - time for plasma outflow from the neck,  = h/2vs , h - height of the neck, h  20r , vs - sound velocity in the neck.

Thermal energy balance in the neck:

d (3NT ) 5 NT B 2 dr  r  QJ  Qrad dt  4 dt 2 I – strength of magnetic field in the neck cr r - radius of plasma column in the neck B

QJ = (I-Ibeam )E –> Joule heating

Electron beam generation in Z-pinch discharges Electron beam generation is due to ‘run-away’ effect, balance equation for number of electrons is as follows: Ibeam – electron beam current; dI beam GNehvb I beam vb -velocity of run-away electrons   vb m vb2 /2 = E* h e. dt g h

Generation function for ‘run-away ‘electrons, from Gurevitch :

Strength of electric field along Z-pinch:

I  I beam E g S 

= ne2/me(ei + eff), ei - electron-ion collision frequency, eff frequency of collisions of electrons with plasma oscillations, S = r2 -cross section of plasma column in the neck region.

Dynamics of plasma parameters, discharge current I=500kA,

Plasma size 0.2-0.7mm

Line emission in time, I=500 kA

W I beam = 20 kA, Er = 2 MV/cm, Ez= 1 MV/cm, possibility to estimate maximal plasma parameters

Ne/1019 H-like

Er, MV/cm Ez, MV/cm

Te, keV R,cm Ibeam,kA

Comparison with experiment Jakubowski, Sadowski, Baronova

Electron beam duration, Delay time of electron beam, Duration of line emission, Plasma size are predicted by the model. 10 ns later

X-ray spectra. Current 150 kA-3 MA.

200 200 kA kA

500 kA Fe K alpha

FeXXV

150 kA 150 kA 200200 kA kA

Current increases => the degree of anisotropy of EVDF decreases

3 MA 360 kA

Angara-5

Plasma dynamics, current 250 kA, 500 kA, 1MA 250 kA

500 kA Ne/e19

Ib,kA

1000 kA

Te,keV E,MV/cm

r,cm U,MV

1. Relative number of runaway electrons are increased with decreasing the discharge current. 2.Strength of electric field is increased with increasing the discharge current 3. Time duration of electron beam& electric fields are increased with decreasing the discharge current. 4. The influence of electron beam on He-like line intensities is decreased with increasing the discharge current, it is not essential even at 500 kA

Conclusion. 1.Equipment is designed and tested on various pinch machines 2. Model is suggested to describe dynamics of plasma parameters. Model is able to predict maximal temperature, density of plasma, etc.