Plasma Laboratory - Weizmann Institute of Science

Measurements of isotropic magnetic fields

Measurements of magnetic fields are of decisive importance in many studies of equilibrium and transient laboratory and space plasmas. If the typical space and time scales of a phenomenon are well within the resolving capabilities of the diagnostics system, a preferred direction of the magnetic field exists. Then, the Zeeman effect can be employed for the magnetic field measurements (e.g., see [1]). When enhanced by using polarization spectroscopy, this approach can also be applied [2] to dense and hot plasmas where the spectral line shapes are dominated by the Stark or Doppler effects. However, if the space or time scales are beyond the resolving capabilities, the magnetic field may have various directions and amplitudes in the region viewed, or the field direction and amplitude may vary significantly during the time of observation. Such "quasi-isotropic" magnetic fields naturally arise in plasmas interacting with electromagnetic energy of very high densities with strong gradients and instabilities, as e.g. in interactions of intense laser beams with matter or in imploding-plasma experiments. Isotropic distributions of magnetic field are also inherent to certain modes of turbulent plasma flow, such as in dynamo generation of galactic fields. Evidently, diagnostic methods that are based on detecting an anisotropy in either the emitted radiation (the Zeeman effect) or in the dispersion properties of the medium (the Faraday rotation) are either inapplicable or provide ambiguous results for such [quasi-]isotropic magnetic fields.

We suggested and implemented [3] a new method for diagnosing such "quasi-isotropic" magnetic fields. The method is based on the fact that different fine-structure components of the same atomic multiplet undergo different splitting in the presence of magnetic field, while the two other major line-broadening mechanisms (the Stark and the Doppler effects) are practically identical for all the multiplet components. This allows a comparison of the line-shapes of such components to be used for determining the magnetic field.

Fig. 1. Zeeman splitting of the 2S1/22P3/2 (solid curves) and the 2S1/22P1/2 (dashed curves) components of a 2S–2P transition, convolved with a small (a) and a dominant (b) Doppler effect (that is assumed to be the same for the two components). Profiles of the σ and π polarizations are given separately. For the comparison, the intensity of the 2S1/22P1/2 component is scaled up by 2 times, to match the intensity of the 2S1/22P3/2 component.

As seen from Fig. 1, the difference between the magnetic-field-induced broadening of the two components is qualitatively preserved for both the σ and π polarizations. Therefore, a difference between the widths of the components of the same multiplet, if observed, is an unambiguous indication of the presence of magnetic field.

For examples of application of the method, see [4] and [5].


  1. Y. Maron, E. Sarid, E. Nahshoni, and O. Zahavi
    Time-dependent spectroscopic observation of the magnetic field in a high-power-diode plasma
    Phys. Rev. A 39, 5856–5862 (1989). DOI BibTeX PDF
  2. G. Davara, L. Gregorian, E. Kroupp, and Y. Maron
    Spectroscopic determination of the magnetic field distribution in an imploding plasma
    Phys. Plasmas 5, 1068–1075 (1998). DOI BibTeX PDF
  3. E. Stambulchik, K. Tsigutkin, and Y. Maron
    Spectroscopic method for measuring plasma magnetic fields having arbitrary distributions of direction and amplitude
    Phys. Rev. Lett. 98, 225001 (2007). DOI BibTeX PDF
  4. S. Tessarin, D. Mikitchuk, R. Doron, E. Stambulchik, E. Kroupp, Y. Maron, D.A. Hammer, V.L. Jacobs, J.F. Seely, B.V. Oliver, and A. Fisher
    Beyond Zeeman spectroscopy: Magnetic-field diagnostics with Stark-dominated line shapes
    Phys. Plasmas 18, 093301 (2011). DOI BibTeX PDF
  5. Blesener, K.S., Pikuz, S.A., Shelkovenko, T.A., Blesener, I.C., Hammer, D.A., Maron, Y., Bernshtam, V., Doron, R., Weingarten, L., and Zarnitsky, Y.
    Measuring magnetic fields in single aluminum wire plasmas with time-resolved optical spectroscopy
    High Energy Density Physics 8, 224–226 (2012). DOI BibTeX

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