Evidence of a Subkinetic Spectral Break in a Strongly Turbulent Collisionless Plasma

Abstract We investigate the magnetic ( B ) and electric ( E ) field spectra in the dissipation range of strong turbulence of a collisionless plasma. This investigation, which is relevant to turbulence studies in many astrophysical settings, is enabled by high-resolution measurements from the four-spacecraft Magnetospheric Multiscale (MMS) mission in the Earth’s magnetotail. B and E spectra are derived as a function of the product of the wave number and electron skin depth ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close="|" open="|"> <mml:mrow> <mml:mi mathvariant="bold-italic">k</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) using a novel technique that employs time-delay analysis on multiple intervals of B and E . Using the MMS tetrahedral formation with close (several d e ) spacing, velocities of B and E signals can be derived so that native frequency-based spectra can be accurately translated to k spectra. The most important finding is a mathematically significant break in the B spectral index that appears at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close="|" open="|"> <mml:mrow> <mml:mi mathvariant="bold-italic">k</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>1</mml:mn> </mml:math> . In the subion range, which spans from the ion inertial length ( d ι ) to d e , the B spectral index is −2.35, then steepens to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>−</mml:mo> <mml:mn>3.13</mml:mn> </mml:math> at sub- d e scales. As expected from previously derived frequency spectra, E has a particularly shallow spectral index (−0.67) in the subion range. At scales smaller than d e and/or the electron thermal gyroradius ( ρ e ), the E spectral index steepens to −2.73. Spectral breaks in both B and E in the dissipation range indicate a change in the physical dissipation processes from ion to electron domination at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close="|" open="|"> <mml:mrow> <mml:mi mathvariant="bold-italic">k</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>1</mml:mn> </mml:math> . We also confirm that at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close="|" open="|"> <mml:mrow> <mml:mi mathvariant="bold-italic">k</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>ρ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> </mml:msub> <mml:mo>&gt;</mml:mo> <mml:mo>~</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mspace width="0.25em"/> </mml:math> the energy density of B and E approaches equipartition, suggesting that energy transfer is near complete.