Table 1 Liouville tracing of the phase-space densities of the crescents in velocity space.

From: Electron Bernstein waves driven by electron crescents near the electron diffusion region

\({W}_{{\rm{e}}}\) [eV]

\({V}_{{\rm{e}}}\) [10\(^{3}\) km s\(^{-1}\)]

\({d}_{{\rm{e}}}\) [km]

\(\Delta {W}_{{\rm{e}}}\) [eV]

\({W}_{{\rm{e}}}^{{\rm{Lt}}}\) [eV]

\({V}_{{\rm{e}}}^{{\rm{Lt}}}\) [10\(^{3}\) km s\(^{-1}\)]

\(\Delta {V}_{{\rm{e}}}\) [10\(^{3}\) km s\(^{-1}\)]

93

5.7

2.4

−42

51

4.2

−1.5

122

6.6

2.9

−48

74

5.1

−1.5

161

7.5

3.4

−56

105

6.1

−1.4

212

8.6

4.1

−62

150

7.2

−1.4

279

9.9

4.8

−71

208

8.5

−1.4

367

11.4

5.7

−80

287

10.0

−1.4

481

13.0

6.7

−81

400

11.8

−1.2

631

14.9

7.8

−83

548

13.9

−1.0

  1. \({W}_{{\rm{e}}}\) and \({V}_{{\rm{e}}}\) denote the electron energy and kinetic velocity, respectively. \({d}_{{\rm{e}}}\) is the gyro-diameter (see Fig. 5b). \(\Delta {W}_{{\rm{e}}}\) and \(\Delta {V}_{{\rm{e}}}\) represent the changes of the electron energy and velocity across the gyro-diameter (see Fig. 5d), while the superscript \({\rm{Lt}}\) denotes the Liouville tracing values
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