7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Pseudo-Maxwellian and Ring Velocity Distributions in Magnetic Reconnection
Shunsuke Usami1,2, Ritoku Horiuchi1
1National Institute for Fusion Science, National Institutes of Natural Sciences,
2
The University of Tokyoe-mail (speaker): usami.shunsuke@nifs.ac.jp

Magnetic reconnection is a fundamental phenomenon
which contains a wide variety of research topics. In order
to investigate various processes associated with magneticreconnection, velocity distributions are analyzed insatellite observations and simulation studies.
Among various types of velocity distributions,ring-shaped velocity distributions are focused on. Ring
velocity distributions are created because of thegyromotion of seed charged particles [1-5]. Let us
consider that seed particles are continuously supplied toa region in which there exist an electric field 𝑬 and amagnetic field 𝑩 causing the 𝐸 × 𝐵 drift with avelocity 𝒗𝑬×𝑩 . In our previous works [3,4], we haveassumed that seed particles have the same initial velocity.
In a velocity space, the orbit of the seed particles is acircle whose center is 𝒗𝑬×𝑩 so that a ring velocity
distribution with no width is formed.
In this work, we consider that seed particles initiallyhave velocity variations [5]. As a plausible case of theseed particles, we postulate a shifted Maxwellian2 )exp[− (𝒗2 ].
velocity distribution (1⁄2𝜋𝑣𝑇0− 𝒗0 )2 ⁄2𝑣𝑇0In
a velocity space, the orbits of the seed particles areconcentric circles whose center is 𝒗𝑬×𝑩 , and hence aring velocity distribution with a width is created. We
formulate a function 𝐺 which expresses a ring
distribution with a width as follows [5]:𝐺(𝒗) =

1𝑉 2 + 𝑣𝑅2𝑉𝑣𝑅
exp[−] 𝐼0 ( 2 ),222𝜋𝑣𝑇02𝑣𝑇0𝑣𝑇0(1)where 𝑣𝑅 = |𝒗0 − 𝒗𝑬×𝑩 | (the circle radius), 𝑉 =|𝒗 − 𝒗𝑬×𝑩 |, and 𝐼𝑛 is the modified Bessel function ofthe first kind. The shape of 𝐺 significantly depends on𝑣𝑅 and 𝑣𝑇0 , Figure 1 shows a bird’s eye view of 𝐺.
We set 𝑣𝑇0 = 0. 3 , 0.5, 0.7 , and 1.0 in the panels(a)-(d), respectively, while 𝑣𝑅 = 1.0 in all the panels. Inthe panels (a) and (b), each shape has a dip in the center,and ring-shape holds. In the panel (c), there is not a dip,
but a plateau in the center. The panel (d) shows that theshape becomes a mountain structure. From Eq. (1), we
analytically derive that if 𝑣𝑇0 > 𝑣𝑅 ⁄√2 , the local
minimum of the ring center changes into the maximum,
and consequently the shape is transformed into maintainstructure. We name it “a pseudo-Maxwellian distribution,”
because it is almost indistinguishable in shape from agenuine Maxwellian distribution.
By using our code “PASMO,” we carry out particle
simulation runs of magnetic reconnection in the presenceof a guide magnetic field. In cases of the guide field ratio
𝐵𝑔 = 2, we find ring-shaped ion velocity distributions
which have a finite width. Next we simulate cases of
𝐵𝑔 = 1, in which ions as the seed particles have a larger

thermal speed, because compressional heating in theupstream region is stronger than the cases of 𝐵𝑔 = 2.
Actually, we observe that mountain-shaped ion velocity
distributions are formed in the downstream. They are toosimilar to a Maxwellian distribution to be distinguishable
in shape, and thus we almost conclude that they arepseudo-Maxwellian distributions.

Figure 1: Brid’s eve view of the function 𝐺 expressedby Eq. 1, (a) for 𝑣𝑇0 = 0. 3, (b) for 𝑣𝑇0 =0.5, (c) for
𝑣𝑇0 = 0.7, and (d) for 𝑣𝑇0 = 1.0.
To completely prove that they are pseudo-Maxwellian
distributions, we show two types of evidence. One is toanalyze the dependence of the distribution shape on theguide magnetic field. The other is to observe velocity
distributions under a hypothetical condition of an
artificial zero temperature in the upstream by utilizing atest particle simulation. From the two types of evidence,
it is definitely confirmed that the mountain-shaped
distributions found in the particle simulations arepseudo-Maxwellian distributions. These results imply
that pseudo-Maxwellian distributions would be createdfor various cases of guide field magnetic reconnection.
For detail, see Ref. [5].
References[1] E. Möbius et al., Nature 318, 426 (1985).
[2] J. F. Drake and M. Swisdak, Phys. Plasmas 21,072903 (2014).
[3] S. Usami, R. Horiuchi, and H. Ohtani, Phys. Plasmas
24, 092101 (2017).
[4] S. Usami, R. Horiuchi, H. Ohtani, Y. Ono, M.
Inomoto, and H. Tanabe, Phys. Plasmas 26, 102103(2019).
[5] S. Usami and R. Horiuchi, Front. Astron. Space Sci. 9,846395 (2022).