# Presentation: 483154

## Simulations of Electron Transport Experiments for Fast Ignition using LSP

**Presented to:**
**15****th**** International Symposium on **
**Heavy Ion Inertial Fusion**
**Princeton University, NJ**
**Richard P. J. Town**
**AX-Division**
**Lawrence Livermore National Laboratory**
**June 7, 2004**

## The LSP code has been used to study fast ignition relevant transport experiments

**A critical issue for Fast Ignition is understanding the transport of the ignitor electrons to the fuel.**
**Experiments have shown a rapid increase in beam width followed by reasonable collimation with a 20****°**** half angle.**
**We have used the LSP code to:**
**generate simulated K******** images; **
**model XUV images; and**
**model cone focus experiments.**
**The LSP code has been used to study the effect on beam transport of:**
**non-Spitzer conductivity; and**
**the initial beam divergence.**

## A critical issue for fast ignition is understanding the transport of the ignitor electrons to the fuel

**Laser couples efficiently**
**to the core**

**Laser couples inefficiently**
**to the core**

**1.1x10****21****cm****-3**

**10****26****cm****-3**

**This is a major driver on the short-pulse laser specification.**

## The XUV image can be used to estimate the temperature of the rear surface

**XUV image**

**A series of *****LASNEX***** calculations of isochorically heated Al targets establishes the relationship between temperature and intensity. **

## Stephens et al.1 used a Bragg crystal mirror to image a Cu fluor layer embedded in Al with a CCD camera

**Fast electron transport is diagnosed by burying a layer of of high-Z (e.g., Cu or Ti)  material within a low-Z plasma matrix (e.g., Al or CH).**
**Electrons reaching the layer cause K-shell ionization and the emitted photons are imaged with a camera, thus characterizing energy transport within a dense plasma.**

**1****R.B. Stephens, et al, to appear in Phys. Rev. E. **

## Experiments on MeV electron transport have been performed by researchers around the world

**Experimental data****1**** show:**
**a rapid increase in beam size in the first few microns; and**
**a fairly collimated (20****o half angle) beam in the bulk of the material.**

**1****M. H. Key, et al, ****5th Workshop on Fast Ignition of Fusion Targets ****(2001).**** **

**0**

**200**

**400**

**200**

**50**

**250**

**150**

**100**

**Thickness (********m)**

**Spot  Radius (********m)**

**X-ray (CH)**

**X-ray (Al)**

**XUV**

**K********  fluorescence**

**Laser spot**

## LSP1 is a hybrid particle code used extensively in the ion beam community

**Performed simulations using 2-D in cylindrical (r-z) geometry.**
**Employs a “direct implicit” energy conserving electromagnetic algorithm.**
**Hybrid fluid-kinetic descriptions for electrons with dynamic reallocation.**
**Scattering between the beam and background plasma included.**
**Ionization and excitation ignored.**
**LSP has been coupled to ITS to enable the generation of**** ****K******** ****images to enable direct comparison with experimental data.**
**Beam created by injection at the target boundary or by promotion within the plasma.**

**1****D. R. Welch, et al, Nucl. Inst. Meth. Phys. Res. A464, 134 (2001).**** **

## We have performed simulations of generic electron transport experiments

**The targets are based on the experiments performed by Martinolli et al****1**** on the LULI and Vulcan laser.**
**The big uncertainty is the initial hot electron beam parameters.**

**1****E. Martinolli, et al., Laser & Part. Beams 20, 171 (2002)****.**** **

## A significant “halo” surrounds the short-pulse high intensity spot

**Typical data from Nova Petawatt laser shows about 30 to 40% of the laser energy in the central spot.**

**We have approximated the laser intensity pattern as two Gaussians.**

## Determining the input electron distribution is based on experimental measurements

**Determining the input electron distribution is based on experimental measurements**

**The conversion efficiency into hot electrons has been measured by many experimentalists over a wide range of intensities:**

****** ****= 0.000175 I(W/cm****2****)****0.2661**

## There are two well-known scaling laws for hot electron temperature which we have used

**There are two well-known scaling laws for hot electron temperature which we have used**

**Pondermotive scaling:**
**T****hot****(MeV)= (I********2****/(10****19****W/cm****2********m****2****))****1/2**
**Beg scaling:**
**T****hot****(MeV)= 0.1(I********2****/(10****17****W/cm****2********m****2****))****1/3**

**Pondermotive**

**Beg**

## The current density and energy distribution can now be defined in terms of laser intensity

**Using the new Python front end to LSP the injected beam energy and current density can be calculated from:**
**conversion efficiency; and**
**hot temperature scaling law.**
**A thermal spread is also added.**

**rold = 0.0**
**for i in range(400):**
**    ****r = (i+0.5)*0.00002**
**    ****intensity = Gaussian(r, 1.0e-3, 1.0e20, 0.0, 1.0e12)**
**                     ****+Gaussian(r, 1.0e-2, 1.0e17, 0.0, 1.0e12)**
**    ****if intensity > 0.0:**
**        ****thot = BegScaling( intensity )**
**        ****ehot ****= 1.6022e-16*thot**
**        ****area = pi*(r**2-rold**2)**
**        ****lpower = intensity*area**
**        ****epower = lpower*conversionEfficiency(intensity)**
**        ****Density**** =1.6022e-19*epower/(area*ehot) **
**    ****rold = r      **

**Pondermotive**

**Beg**

## The LSP code uses Spitzer conductivity, which we know is not valid at low temperatures.

**The calculated resistivity of aluminum at solid density *****increases***** with temperature.**

**10****-8**

**10****-7**

**10****-6**

**10****-5**

**10****-1**

**10****0**

**10****1**

**10****2**

**10****3**

**Temperature (eV)**

**Resistivity (********m)**

**Spitzer**

**Non-Spitzer**

## Reduced filamentation is observed when the conductivity is constant to 100eV

**Beam density at 1.6 ps**

## The K diagnostic gives time-integrated images of the emission generated by the hot electron beam 

**The diagnostic will record both K******** photons generated by the forward going and backward going “refluxed” electrons.**

## K images were generated at various times throughout the simulations

**A time history displaying the birth positions of the K******** photons can be generated for each source.**

**Photons created ******** 0.5ps**

****** ****1.5ps**

****** ****3.0ps**

**Base source case:  Beg Temperature Scaling, 200keV transverse thermal energy**

**X (********m)**

**X (********m)**

**R (microns)**

**X (********m)**

**Y (********m)**

**Y (********m)**

**Y (********m)**

**The time integrated diagnostic is a good **
**measure of hot electron beam**** transport.**

## LSP calculations show reasonable agreement with experimental data for moderate Al thicknesses 

**There appears to be moderate agreement in the trend of increasing spot diameter with Al thickness, based on the average between vertical and horizontal line-outs.**
**The large asymmetry in the horizontal direction is under investigation.**

**Spot Diameter (********m)**

**Experimental Data**

**LSP calculations**

**Al Thickness (********m)**

## We can also compare these source scenarios using the K spot diameter at half-max intensity

**A significant asymmetry was detected when taking similar line-outs in the horizontal direction, resulting in the relatively large error in spot diameter for many of the data points.**

**140**
**120**
**100**
**80**
**60**
**40**
**20**
**0**

**2D Source Injection**

**Spot Diameter (microns)**

**Thermal transverse temperature (keV)**

**(I********2****)****3/2**

**(I********2****)****1/2**

** ****(I********2****)****1/3**

**0     100    200    300    400    500    600**

**140**
**120**
**100**
**80**
**60**
**40**
**20**
**0**

**Spot Diameter (********m)**

## The LSP calculation matches  the measured temperature pattern at the rear surface of the target

**27J of hot electrons, in a 1-ps pulse, with Beg scaling and a thermal spread of 300keV injected into a 100********m Al****3+ ****plasma.**
**The temperature was obtained by post-processing the LSP energy data at the rear surface with a realistic equation of state.**

## Z3 is being used to generate hot electrons from LASNEX-predicted pre-pulse plasmas

**1-D line out of plasma formed by 10mJ prepulse on a CH target:**
**(z,x) plots of electrons with energies > 12 MeV:**

**0.5 ps**

**1.0 ps**

**UCRL-PRES-204413-20**

## Extracting the correct electron distribution function is more complicated for oblique incidence

**Extracting the correct electron distribution function is more complicated for oblique incidence**

**A 10****19**** W/cm****2**** laser incident on a 16 n****c**** plasma (shown by white lines) at a 30****o**** angle of incidence.**
**(z,x) phase space plot of  electrons with energies      > 5 MeV.**

**0.3 ps**

**0.6 ps**

**Electrons**
**injected at**
**a significant**
**angle**

**We are using Python to closely **
**couple Z3 output to LSP input**

**0.5 ps**

**0.3 ps**

## We have recently started large scale cone calculations using LSP

**Background electron density profile of a gold cone touching a perfect conductor.**

**2MeV electrons**
**promoted**
**along surface**

## Hot electrons start on inner edge and then diffuse into the cone

**0.16 ps**

**1.4 ps**

**Transport efficiency <20% of hot electron out of cone**

## The LSP code has been used to study fast ignition relevant transport experiments

**A critical issue for Fast Ignition is understanding the transport of the ignitor electrons to the fuel.**
**Experiments have shown a rapid increase in beam width followed by reasonable collimation with a 20****°**** half angle.**
**We have used the LSP code to:**
**generate simulated K******** images; **
**model XUV images; and**
**model cone focus experiments.**
**The LSP code has been used to study the effect on beam transport of:**
**non-Spitzer conductivity; and**
**the initial beam divergence.**

## Collaborators:

**C. Chen, L. A. Cottrill, M. H. Key, W. L. Kruer, A. B. Langdon, **
**B. F. Lasinski, B. C. McCandless, R. A. Snavely, C. H. Still, **
**M. Tabak****, S. C. Wilks, **
***LLNL, Livermore, CA, USA.***
**D. R. Welch, **
**MRC,***** Albuquerque, NM, USA.***