Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T00:41:53.573Z Has data issue: false hasContentIssue false
  • English
  • Français

Proton imaging of 3D density distribution for dense DT plasmas using regularization method

Published online by Cambridge University Press:  12 February 2016

Xuemei Li  and
Yuhua Wang
Xuemei Li*
Affiliation:
Physical Experiment Center, Zhejiang Ocean University, Zhoushan, Zhejiang 316022, China
Yuhua Wang
Affiliation:
School of Petrochemical and Energy Engineering, Zhejiang Ocean University, Zhoushan, Zhejiang 316022, China
*
Address correspondence and reprint requests to: Xuemei Li, Physical Experiment Center, Zhejiang Ocean University, Zhoushan, Zhejiang 316022, China. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Three-dimensional (3D) density distribution of inhomogeneous dense deuterium tritium plasmas in laser fusion is revealed by the energy loss of fast protons going through the plasmas. The fast protons generated in the laser–plasma interaction can be used for the simulation of a plasma density diagnostics. The large linear and ill-posed equation set of the densities of all grids is obtained and then solved by the Tikhonov regularization method after dividing a 3D area into grids and knowing the initial and final energies of the protons. 3D density reconstructions with six proton sources are done without and with random noises added to the final energy. The revealed density is a little smaller than the simulated one in most simulated zones and the error is as much as those of 2D reconstructions with four proton sources. The picture element N is chosen as 2744 with consideration of smoothness and calculation memory of the computers. With fast calculation speed and low error, the Tikhonov regularization method is more suitable for 3D density reconstructions with large calculation amount than simultaneous iterative reconstruction method. Also the analytical expressions between the errors and the noises are established. Furthermore, the density reconstruction method in this paper is particularly suitable for plasmas with small density gradient. The errors without noises and with 2% noises added to the final proton energies are 3 and 20%, respectively, for the homogeneous plasma.

Keywords

DT plasmaFast protonsReconstructionThree-dimensional density distributionTikhonov regularization method
Type
Research Article
Information
Laser and Particle Beams , Volume 34 , Issue 2 , June 2016 , pp. 210 - 218
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Atzeni, S. & Meyer-Ter-vehn, J. (2004). The Physics of Inertial Fusion: Beam Plasma Interaction, Hydrodynamics, Hot Dense Matter. Oxford: Oxford Science.CrossRefGoogle Scholar
Borghesi, M., Audebert, P., Bulanov, S.V., Cowan, T., Fuchs, J., Gauthier, J.C., Mackinnon, A.J., Patel, P.K., Pretzler, G., Romagnani, L., Schiavi, A., Toncian, T. & Willi, O. (2005). High-intensity laser-plasma interaction studies employing laser driven proton probes. Laser Part. Beams 23, 291–295.CrossRefGoogle Scholar
Borghesi, M., Kar, S., Romagnani, L., Toncian, T., Antici, P., Audebert, P., Brambrink, E., Ceccherini, F., Cecchetti, C.A., Fuchs, J., Galimberti, M., Gizzi, L.A., Grismayer, T., Lyseikina, T., Jung, R., Macchi, A., Mora, P., Osterholtz, J., Schiavi, A. & Willi, O. (2007). Impulsive electric fields driven by high-intensity laser matter interactions. Laser Part. Beams 25, 161–167.Google Scholar
Borghesi, M., Schiavi, A., Campbell, D.H., Haines, M.G., Willi, O., Mackinnon, A.J., Gizzi, L.A., Galimberti, M., Clarke, R.J. & Ruhl, H. (2001). Proton imaging: A diagnostic for inertial confinement fusion/fast ignitor studies. Plasma Phys. Control. Fusion 43, A267–A276.Google Scholar
Califano, F., Pegoraro, F. & Bulanov, S.V. (2003). Propagation of a short proton beam through a thin plasma slab. Phys. Rev. E 68, 066406.CrossRefGoogle Scholar
Christopher, G.S. (2007). Radiochromic film dosimetry. Radiat. Meas. 41, S100–S116.Google Scholar
Fernández-Martínez, J.L., Pallero, J.L.G., Fernández-Muñiz, Z. & Pedruelo-González, L.M. (2014). The effect of noise and tikhonov's regularization in inverse problems. part i: The linear case. J. Appl. Geophys. 108, 176–185.Google Scholar
Flippo, K., Hegelich, B.M., Albright, B.J., Yin, L., Gautier, D.C., Letzring, S., Schollmeier, M., Schreiber, J., Schulze, R. & Fernandez, J.C. (2007). Laser-driven ion accelerators: Spectral control, monoenergetic ions and new acceleration mechanisms. Laser Part. Beams 25, 3–8.Google Scholar
Fourkal, E., Velchev, I. & Ma, C.M. (2005). Coulomb explosion effect and the maximum energy of protons accelerated by high-power lasers. Phys. Rev. E 71, 036412.Google Scholar
Fox, W., Fiksel, G., Bhattacharjee, A., Chang, P.Y., Germaschewski, K., Hu, S.X. & Nilson, P.M. (2013). Filamentation instability of counterstreaming laser-driven plasmas. Phys. Rev. Lett. 111, 2909–2915.Google Scholar
Gao, L., Nilson, P.M., Igumenschev, I.V., Fiksel, G., Yan, R., Davies, J.R., Martinez, D., Smalyuk, V., Haines, M.G., Blackman, E.G., Froula, D.H., Betti, R. & Meyerhofer, D.D. (2013). Observation of self-similarity in the magnetic fields generated by the ablative nonlinear Rayleigh-Taylor instability. Phys. Rev. Lett. 110, 368–371.Google Scholar
Golubev, A., Basko, M., Fertman, A., Kozodaev, A., Mesheryakov, N., Sharkov, B. & Vishnevskiy, A. (1998). Dense plasma diagnostics by fast proton beams. Phys. Rev. E 57, 3363–3367.Google Scholar
Hegelich, B.M., Albright, B.J., Cobble, J., Flippo, K., Letzring, S., Paffett, M., Ruhl, H., Schreiber, J., Schulze, R.K. & Fernã¡ndez, J.C. (2006). Laser acceleration of quasi-monoenergetic MeV ion beams. Nature 439, 441–444.CrossRefGoogle ScholarPubMed
Honerkamp, J. & Weese, J. (1990). Tikhonovs regularization method for ill-posed problems. Contin. Mech. Thermodyn. 2, 17–30.Google Scholar
Lancia, L., Albertazzi, B., Boniface, C., Grisollet, A., Riquier, R., Chaland, F., Le Thanh, K.C., Mellor, P., Antici, P., Buffechoux, S., Chen, S.N., Doria, D., Nakatsutsumi, M., Peth, C., Swantusch, M., Stardubtsev, M., Palumbo, L., Borghesi, M., Willi, O., Pépin, H. & Fuchs, J. (2014). Topology of megagauss magnetic fields and of heat-carrying electrons produced in a high-power laser-solid interaction. Phys. Rev. Lett. 113, 235001–235001.Google Scholar
Levy, M.C., Ryutov, D.D., Wilks, S.C., Ross, J.S., Huntington, C.M., Fiuza, F., Martinez, D.A., Kugland, N.L., Baring, M.G. & Park, H.-S. (2015). Development of an interpretive simulation tool for the proton radiography technique. Rev. Sci. Instrum. 86, 033302.Google Scholar
Li, X.M., Shen, B.F., Zhang, X.M., Jin, Z.Y. & Wang, F.C. (2008). The diagnostics of density distribution for inhomogeneous dense DT plasmas using fast protons. Laser Part. Beams 26, 139–145.Google Scholar
Li, X.M., Shen, B.F., Zhang, X.M., Jin, Z.Y. & Wang, F.C. (2011). SIRT method for diagnostics of inhomogeneous dense DT plasmas with fast proton. Chin. J. Comput. Phys. 28, 75–80.Google Scholar
Liu, J.Z., Liu, L.T., Liang, X.H. & Ye, Z.R. (2015). 3D density inversion of gravity gradient data using the extrapolated tikhonov regularization. Appl. Geophys. 12, 1–10.CrossRefGoogle Scholar
Livingston, M.S. & Beth, H.A. (1937). Nuclear physics C. nuclear dynamics, experimental. Rev. Mod. Phys. 9, 000245.Google Scholar
Mackinnon, A.J., Patel, P.K., Borghesi, M., Clarke, R.C., Freeman, R.R., Habara, H., Hatchett, S.P. & Hey, D., Hicks, D.G., Kar, S., Key, M.H., King, J.A., Lancaster, K., Neely, D., Nikkro, A., Norreys, P.A., Notley, M.M., Phillips, T.W., Romagnani, L., Snavely, R.A., Stephens, R.B. & Town, R.P.J. (2006). Proton radiography of a laser-driven implosion. Phys. Rev. Lett. 97, 045001.Google Scholar
Mclaughlin, W.L., Chen, Y.D., Soares, C.G., Miller, A., Van Dyk, G. & Lewis, D.F. (1991). Sensitometry of the response of a new radiochromic film dosimeter to gamma radiation and electron beams. Nucl. Instrum. Methods Phys. Res. A-Accel. Spectrom. Detect. Assoc. Equip. 302, 165–176.Google Scholar
Morgan, C.A., Griem, H.R. & Elton, R.C. (1994). Spectroscopic measurements of electron density and temperature in polyacetal-capillary-discharge plasmas. Phys. Rev. E 49, 2282–2291.Google Scholar
Nichiporov, D., Kostjuchenko, V., Puhl, J.M., Bensen, D.L., Desrosiers, M.F., Dich, C.E., Mclaughlin, W.L., Kojima, T., Coursey, B.M. & Zink, S. (1995). Investigation of applicability of alanine and radiochromic detectors to dosimetry of proton clinical beams. Appl. Radiat. Isot. 46, 1355–1362.Google Scholar
Smith, J.H. (1947). Theoretical range-energy values for protons in air and aluminum. Phys.Rev. 71, 32–33.Google Scholar
Snyder, S.C., Crawford, D.M. & Fincke, J.R. (2000). Dependence on the scattering angle of the electron temperature and electron density in Thomson-scattering measurements on an atmospheric-pressure plasma jet. Phys. Rev. E. 61, 1920–1924.Google Scholar
Wang, X. (2007). Research and implementation on the 3D reconstruction Technology of Medical CT image. Master Thesis. Wuhan: Huazhong University of Science & Technology.Google Scholar
Willi, O., Toncian, T., Borghesi, M., Fuchs, J., D'Humieres, E., Antici, P., Audebert, P., Brambrink, E., Cecchetti, C., Pipahl, A. & Romagnani, L. (2007). Laser triggered micro-lens for focusing and energy selection of MeV protons. Laser Part. Beams 25, 71–77.Google Scholar
Xiao, T.Y., Yu, S.G. & Wang, Y.F. (2003). The regularization method based on the variational principle. In The Numerical Computation for the Inverse Problems, (Shi, Z.C. and Li, Y.S., Eds), pp. 18–37. Beijing: The Science Press of China.Google Scholar
Yin, L., Albright, B.J., Hegelich, B.M. & Fernandez, J.C. (2006). GeV laser ion acceleration from ultrathin targets: The laser break-out afterburner. Laser Part. Beams 24, 291–298.Google Scholar
Zhang, H., Lin, Z.Q. & Bi, W.J. (1987). Measurement of electron density profile in a laser-produced plasma. Acta Opt. Sin. 7, 36–42.Google Scholar
Zhang, X., Shen, B., Li, X., Jin, Z. & Wang, F. (2007). Multistaged acceleration of ions by circularly polarized laser pulse: Monoenergetic ion beam generation. Phys. Plasmas 14, 073101.Google Scholar