Skip to main content
SpringerLink
Log in

Transport of Charged Particles

  • Chapter
  • First Online:
Monte Carlo Methods for Radiation Transport

Part of the book series: Biological and Medical Physics, Biomedical Engineering ((BIOMEDICAL))

  • 1760 Accesses

Abstract

Charged particles that play an important role in radiotherapy include electrons, positrons, protons, and carbon ions. Other ions with relatively small atomic numbers are presently being considered as possible alternatives to proton and carbon-ion beams. Charged heavy recoils can also be produced in nuclear reactions. This effect can be significant and should be accounted for in dose calculations for hadrontherapy.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Abramowitz, M., Stegan I.A. (eds.): Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables. Dover Publications, New York (1964)

    MATH  Google Scholar 

  • Aghili, A., Moghaddam, B.P.: Certain theorems on two dimensional Laplace transform and non-homogeneous parabolic partial differential equations. Surv. Math. Appl. 6, 165–174 (2011)

    MathSciNet  Google Scholar 

  • Arfken, G.B.: Mathematical Methods for Physicists, 3rd edn. Academic, New York (1985)

    MATH  Google Scholar 

  • Arfken, G.B., Weber, H.J., Harris, F.E.: Mathematical Methods for Physicists, 7th edn. Elsevier, Amsterdam (2013)

    MATH  Google Scholar 

  • Bargmann, V.: On the number of bound states in a central field of force. Proc. Natl. Acad. Sci. 38 (11), 961–966 (1952)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Baron, E.: Beam-stripper interaction studies for GANIL. IEEE Trans. Nucl. Sci. 26 (2), 2411–2413 (1979)

    Article  ADS  Google Scholar 

  • Bernal, M.A., Bordage, M.C., Brown, J.M.C., Davidkova, M., Delage, E., El Bitar, Z., Enger, S.A., Francis, Z., Guatelli, S., Ivanchenko, V.N., Karamitros, M., Kyriakou, I., Maigne, L., Meylan, S., Murakami, K., Okada, S., Payno, H., Perrot, Y., Petrovic, I., Pham, Q.T., Ristic- Fira, A., Sasaki, T., Stepan, V., Tran, H.N., Villagrasa, C., Incerti, S.: Track structure modeling in liquid water: a review of the Geant4-DNA very low energy extension of the Geant4 Monte Carlo simulation toolkit. Phys. Med. 31 (8), 861–874 (2015)

    Google Scholar 

  • Bethe, H.A.: Molière’s theory of multiple scattering. Phys. Rev. 89 (6), 1256–1266 (1953)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Brandt, W., Kitagawa, M.: Effective stopping-power charges of swift ions in condensed matter. Phys. Rev. B 25 (9), 5631–5637 (1982)

    Article  ADS  Google Scholar 

  • Bridwell, L.B., Cowern, N.E.B., Read, P.M., Sofield, C.J.: Measurement of polarization, Bloch and charge exchange contributions to the stopping power of C and O ions in carbon. Nucl. Instrum. Meth. B 13 (1–3), 123–126 (1986)

    Google Scholar 

  • Bouchard, H., Bielajew, A.: Lorentz force correction to the Boltzmann radiation transport equation and its implications for Monte Carlo algorithms. Phys. Med. Biol. 60 (13), 4963–4971 (2015)

    Article  Google Scholar 

  • Datz, S., Appleton, B.R., Moak, C.D. (eds.): Atomic Collisions in Solids. Springer, Berlin (1975)

    Google Scholar 

  • Echenique, P.M., Flores, F., Ritchie, R.H.: Dynamic screening: capture and loss processes of protons moving in solids. Nucl. Instrum. Meth. B B33 (1–4), 91–97 (1988)

    Article  ADS  Google Scholar 

  • Gervasoni, J.L., Cruz-Jimenez, S.: Bohr’s adiabatic criterion and effective charge of heavy ions. Radiat. Phys. Chem. 48 (4), 433–436 (1996)

    Article  ADS  Google Scholar 

  • Goudsmit, S., Saunderson, J.L.: Multiple scattering of electrons. Phys. Rev. 57 (1), 24–29 (1940a)

    Article  ADS  MATH  Google Scholar 

  • Goudsmit, S., Saunderson, J.L.: Multiple scattering of electrons. II. Phys. Rev. 58, 36–42 (1940b)

    Article  ADS  MATH  Google Scholar 

  • Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series and Products, Corrected and Enlarged Edition. Academic, San Diego (1980)

    MATH  Google Scholar 

  • Incerti, S., Baldacchino, G., Bernal, M., Capra, R., Champion, C., Francis, Z., Guatelli, S., Guye, P., Mantero, A., Mascialino, B., Moretto, P., Nieminen, P., Villagrasa, C., Zacharatou, C.: The Geant4-DNA project. Int. J. Model. Simul. Sci. Comput. 1, 157–178 (2010)

    Article  Google Scholar 

  • Jackson, J.D.: Classical Electrodynamics. 3rd edn. Wiley, New York (1999)

    MATH  Google Scholar 

  • Jenkins, T.M., Nelson, W.R., Rindi, A., Nahum, A.E., Rogers, D.W.O., Bielajew, A.F. (eds.): Monte Carlo Transport of Electrons and Photons. Plenum Press, New York (1988)

    Google Scholar 

  • Kaneko, T: Energy loss of protons and helium ions passing through matter. Phys. Rev. A 33 (3), 1602–1611 (1986)

    Article  ADS  Google Scholar 

  • Keyvanloo, A., Burke, B., Warkentin, B., Tadic, T., Rathee, S., Kirkby, C., Santos, D.M., Fallone, B.G.: Skin dose in longitudinal and transverse linac-MRIs using Monte Carlo and realistic 3D MRI field models. Med. Phys. 39 (10), 6509–6521 (2012)

    Article  Google Scholar 

  • Kirkby, C., Murray, B., Rathee, S., Fallone, B.G.: Lung dosimetry in a linac-MRI radiotherapy unit with a longitudinal magnetic field. Med. Phys. 37 (9), 4722–4732 (2010)

    Article  Google Scholar 

  • Kreussler, S., Varelas, C., Brandt, W.: Target dependence of effective projectile charge in stopping powers. Phys. Rev. B 23 (1), 82–84 (1981)

    Article  ADS  Google Scholar 

  • Landau, L.: On the energy loss of fast particles by ionisation. J. Phys. 8 (1–6):201–205 (1944)

    Google Scholar 

  • Larsen, E.W.: A theoretical derivation of the condensed history algorithm. Ann. Nucl. Energy 19 (10–12), 701–714 (1992)

    Article  Google Scholar 

  • LePage, W.R.: Complex Variables and the Laplace Transform for Engineers. Dover Publications, New York (2010)

    Google Scholar 

  • Lewis, H.W.: Multiple scattering in an infinite medium. Phys. Rev. 78 (5), 526–529 (1950)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Macdonald, H.M.: The Addition theorem for the Bessel functions. Proc. Lond. Math. Soc. s1–32 (1):152–157 (1900)

    Google Scholar 

  • Molière, G.: Theorie der Streuung schneller geladener Teilchen I. Einzelstreuung am abgeschirmten Coulomb-Feld. Z. Naturforsch A 2 (3), 133–145 (1947)

    MATH  Google Scholar 

  • Molière, G.: Theorie der Streuung schneller geladener Teilchen II. Mehrfach- und Vielfachstreuung. Z. Naturforsch A 3 (2), 78–97 (1948)

    ADS  Google Scholar 

  • Nikjoo, H., Uehara S., Emfietzoglou D., Brahme A.: Heavy charged particles in radiation biology and biophysics. New J. Phys. 10, 075006 (2008)

    Article  ADS  Google Scholar 

  • Poularikas, A.D. (ed.): Transforms and Applications Handbook. 3rd edn. CRC Press, Boca Raton, FL (2010)

    MATH  Google Scholar 

  • Raaijmakers, A.J.E., Raaymakers, B.W., van der Meer, S., Lagendijk, J.J.W.: Integrating a MRI scanner with a 6 MV radiotherapy accelerator: impact of the surface orientation on the entrance and exit dose due to the transverse magnetic field. Phys. Med. Biol. 52 (4), 929–939 (2007)

    Article  Google Scholar 

  • Rogers, F.J., Graboske, H.C., Harwood, D.J.: Bound eigenstates of the static screened Coulomb potential. Phys. Rev. A 1 (6), 1577–1586 (1970)

    Article  ADS  Google Scholar 

  • Rutherford, E.: The scattering of α and β particles by matter and the structure of the atom. Philos. Mag. 21 (125), 669–688 (1911)

    Article  MATH  Google Scholar 

  • Sabin, J.R., Brandas, E. (eds.): Advances in Quantum Chemistry. Theory of Interactions of Swift Ions with Matter. Part 2. Elsevier, Amsterdam (2004)

    Google Scholar 

  • Salvat, F., Fernandez–Varea, J.M., Sempau, J.: PENELOPE-2011. A code system for Monte Carlo simulation of electron and photon transport: Nuclear Energy Agency (2011)

    Google Scholar 

  • Shima, K., Nakagawa E., Kakita T., Yamanouchi M, Awaya Y., Kambara T., Mizogawa T., Kanai Y.: Projectile atomic number dependence of equilibrium charge states for 1 and 2 MeV ions passing through a carbon foil. Nucl. Instrum. Meth. B B33 (1–4), 212–215 (1988)

    Article  ADS  Google Scholar 

  • St. Aubin, J., Keyvanloo, A., Vassiliev, O., Fallone, B.G.: A deterministic solution of the first order linear Boltzmann transport equation in the presence of external magnetic fields. Med. Phys. 42 (2), 780–793 (2015)

    Google Scholar 

  • St. Aubin, J., Keyvanloo, A., Fallone, B.G.: Discontinuous finite element space-angle treatment of the first order linear Boltzmann transport equation with magnetic fields: application to MRI-guided radiotherapy. Med. Phys. 43 (1), 195–204 (2016)

    Google Scholar 

  • Vavilov, P.V.: Ionization losses by high-energy heavy particles. Sov. Phys. JETP 5 (4), 749–751 (1957)

    Google Scholar 

  • Wang, H., Vassiliev, O.N.: Microdosimetric characterisation of radiation fields for modelling tissue response in radiotherapy. Int. J. Cancer Ther. Oncol. 2 (1), 020116 (2014)

    Article  Google Scholar 

  • Yang, Y.M., Bednarz, B.: Consistency evaluation between EGSnrc and Geant4 charged particle transport in an equilibrium magnetic field. Phys. Med. Biol. 58 (4), N47–N58 (2013)

    Article  Google Scholar 

  • Zaikov, V.P., Kral’kina, E.A., Vorobjev, N.F., Dmitriev, I.S., Nikolaev, V.S., Teplova, Y.A.: Attainment of equilibrium charge distributions in fast ion beams passing through solid films. Nucl. Instr. Meth. B 5 (1), 10–13 (1984)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, Houston, TX, USA

    Oleg N. Vassiliev

Authors
  1. Oleg N. Vassiliev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Vassiliev, O.N. (2017). Transport of Charged Particles. In: Monte Carlo Methods for Radiation Transport. Biological and Medical Physics, Biomedical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-44141-2_5

Download citation

Publish with us

Policies and ethics

Search

Navigation