Electron and Proton Energization in 3D Reconnecting Current Sheets in Semirelativistic Plasma with Guide Magnetic Field

In many plasma environments, magnetic energy is converted to plasma energy at thin current sheets (CSs), likely via magnetic reconnection (e.g., Zweibel & Yamada 2009). Reconnection occurs in diverse regimes and, even in 2D, generates such complexity that we owe much of our understanding to numerical simulation. Unfortunately, 3D simulation studies are far costlier than 2D, motivating efforts to understand similarities between 2D and 3D reconnection and more generally to understand 3D CS evolution in terms of 2D processes whenever possible.

A thin CS, considered in 2D (specifically in "2Dxy," the x–y plane perpendicular to the current j_z supporting a magnetic field $\hat{{\boldsymbol{x}}}{B}_{0}\tanh (y/\delta )$ reversing over thickness 2δ), will typically be most unstable to tearing, leading, in its nonlinear stage, to reconnection and rapid magnetic energy release. In 2Dyz, the same CS may kink or ripple due to the drift-kink instability (DKI), which in its nonlinear stage induces severe contortions that rapidly release magnetic energy (e.g., Pritchett et al. 1996). The DKI requires two counterdrifting species and hence is not a magnetohydrodynamic (MHD) instability; it is important when the separation between electron and ion scales is small (Daughton 1999; Hesse & Birn 2000; Scholer et al. 2003), or absent as in relativistic pair plasma (Zenitani & Hoshino 2005, 2008; Yin et al. 2008; Liu et al. 2011; Cerutti et al. 2014; Guo et al. 2014, 2015). In 3D, these instabilities can compete and interact. Although 2D-like reconnection may dominate DKI in 3D (Kagan et al. 2013; Cerutti et al. 2014; Guo et al. 2014, 2015, 2021; Sironi & Spitkovsky 2014; Werner & Uzdensky 2017), Werner & Uzdensky (2021) highlighted how the DKI can dramatically slow reconnection. Furthermore, in 3D only, flux ropes formed by reconnection can decay via the MHD kink instability (Kagan et al. 2013; Markidis et al. 2014; Zhang et al. 2021b; Schoeffler et al. 2023), releasing additional magnetic energy (Werner & Uzdensky 2021).

Using particle-in-cell (PIC) simulation, this work characterizes energy conversion as a function of guide magnetic field, in 3D CSs in magnetically dominated, collisionless electron–proton plasma, with true mass ratio μ = 1836, in the semirelativistic regime. In semirelativistic plasma, where electrons are ultrarelativistic and protons subrelativistic, relativistic effects diminish the scale separation between (e.g., gyroradii of) electrons and ions (protons), making DKI consequential. The semirelativistic regime is one of the several important regimes for black hole (BH) accretion flows, which are expected to have electron–ion plasma at temperatures around 10–100 MeV (e.g., Dexter et al. 2020) and likely develop large, complicated, turbulent magnetic field structures in the accretion flow, in the overlying corona/wind, and in and around the jet (e.g., Galeev et al. 1979; Uzdensky & Goodman 2008; Ripperda et al. 2020; Chashkina et al. 2021; Bacchini et al. 2022; Zhdankin et al. 2023). We generally expect CS formation and reconnection in such contexts, and the resulting particle energization could potentially power flaring emission in BHs (as in solar flares). Furthermore, characterizing electron and ion energization in the semirelativistic regime is crucial for global MHD modeling of reconnection-powered emission from accreting BHs (Chael et al. 2018; Dexter et al. 2020; Ressler et al. 2020, 2023; Hankla et al. 2022; Scepi et al. 2022).

Until now (to our knowledge), no 3D PIC studies of electron–ion reconnection (or CS evolution) have characterized energy conversion in the nonradiative semirelativistic regime (N.B., Chernoglazov et al. 2023 includes 1% ultrarelativistic ions among positrons and electrons, with radiative cooling), although several 2D reconnection studies have (Melzani et al. 2014a, 2014b; Guo et al. 2016; Rowan et al. 2017; Ball et al. 2018, 2019; Werner et al. 2018; Rowan et al. 2019).

After describing the simulation setup (Section 2), we will focus on the different energy components, discussing the release of magnetic energy U_Bxy (Section 3), the increase in guide-field energy U_Bz (Section 4), the electric field energy U_E (Section 5), and the electron and ion energies U_e + U_i = U_ptcl (Section 6). We summarize in Section 7.

Simulations were run with the Zeltron electromagnetic PIC code (Cerutti et al. 2013), initialized with semirelativistic electron–proton plasma in a standard Harris sheet configuration with uniform background plasma (similar to Werner et al. 2018)—initial physical and numerical parameters are listed in Table 1. By "semirelativistic" we mean that ions remain subrelativistic while electrons are ultrarelativistic and experience ultrarelativistic energy gains; in terms of quantities in Table 1, m_e c² ≪ T_b ≪ m_i c² and σ_i ≪ 1 ≪ σ_e . The simulation frame (with zero initial electric field) is the zero-momentum frame, where ions drift slowly and electrons carry the current supporting the field reversal.

Table 1. Initial Plasma and Numerical Simulation Parameters

μ ≡ mi /me = 1836	ion/electron mass ratio
B0	asymptotic upstream (reversing) magnetic field
nb = nbe = nbi	background electron/ion density
Tb = 18.36me c2 = 0.01mi c2	background electron/ion temperature
${\sigma }_{i}\equiv {B}_{0}^{2}/(4\pi {n}_{b}{m}_{i}{c}^{2})=0.5$	background ion cold magnetization
${\sigma }_{e}\equiv {B}_{0}^{2}/(4\pi {n}_{b}{m}_{e}{c}^{2})=\mu {\sigma }_{i}=918$	background electron cold magnetization
δ = 0.33σi ρi0	Harris CS half-thickness (ρi0 ≡ mi c2/eB0)
${\boldsymbol{B}}(y)=\hat{{\boldsymbol{z}}}{B}_{{gz}}-\hat{{\boldsymbol{x}}}{B}_{0}\tanh (y/\delta )$	magnetic field profile
$-0.6c\hat{{\boldsymbol{z}}}$, $+0.0004c\hat{{\boldsymbol{z}}}$	electron, ion bulk drift velocities in CS
$\eta \equiv {n}_{d,\max }/{n}_{b}=5$	CS overdensity
${n}_{d}(y)=\eta {n}_{b}{\cosh }^{-2}(y/\delta )$	CS electron/ion density profile
Td = 51me c2 = 0.28mi c2	CS electron/ion (comoving) temperature
${\beta }_{{be}}={\beta }_{{bi}}\equiv 8\pi {n}_{b}{T}_{b}/{B}_{0}^{2}=0.04$	upstream plasma beta for electrons/ions
vA = 0.57c	upstream Alfvén velocity for Bgz = 0
Ly ≡ L = 55.3σi ρi0	system size (in y)
Lx /L = 1	system x/y aspect ratio (for 2Dxy and 3D)
${L}_{z}/L=\max (1,{B}_{{gz}}/{B}_{0})$	system z/y aspect ratio (for 2Dyz and 3D)
T = 20L/c	simulation duration
Δy = Δz = 0.036σi ρi0	grid cell size in y and z
Δx = 0.058σi ρi0	grid cell size in x
Δt = 0.64Δy/c	time step (the 3D Courant–Friedrichs–Lewy maximum)
Mppcs = 10 (3D), 160 (2D)	macroparticles per cell per species (four species)
Mppcs = 40 (3D), 640 (2D)	total macroparticles per cell

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The initial CS is perpendicular to y, with current in the +z direction and reversing magnetic field in the ±x directions (approaching value B₀ upstream). We add uniform guide field ${B}_{{gz}}\hat{{\boldsymbol{z}}}$, exploring several strengths B_gz /B₀ ∈ {0, 0.25, 0.5, 1, 2, 4} (except B_gz /B₀ = 4 was not run in 3D, due to expense). We also explore three dimensionalities: 2Dxy (2D simulation ignoring z—classic 2D reconnection), 2Dyz (ignoring x, for studying DKI), and full 3D. Also, in one case, 2Dyz and B_gz = 0, we ran an ensemble of three simulations, identical except for differing randomization of initial particles.

Table 2 lists length scales of interest in terms of σ_i ρ_i0 = σ_e ρ_e0, where ρ_s0 ≡ m_s c²/(eB₀); σ_e ρ_e0 is the gyroradius of an "energized" electron with energy $2{B}_{0}^{2}/(8\pi {n}_{{be}})$ in perpendicular field B₀.

The system size, containing a single CS, is L ≡ L_y = 55.3σ_i ρ_i0 and L_x = L_z = L (except when B_gz > B₀, we increase L_z = (B_gz /B₀)L_y ; and 2D simulations lack either the x or z dimension). Boundary conditions are periodic in x and z, and conducting/particle-reflecting in y. The size L is large with respect to initial kinetic scales and CS thickness (e.g., L/(2δ) = 83), and L > 20σ_i ρ_i0 puts it in the "large system regime" as defined by Werner et al. (2016), albeit for relativistic pair plasma in 2Dxy

We empirically found that using anisotropic grid cells with Δx/1.6 = Δy = Δz = σ_i ρ_i0/28 avoids numerical instabilities while yielding the best computational performance. We similarly found that the number of computational macroparticles (each representing many physical particles) needed to avoid unphysical electron–ion energy exchange at late times was 160 per cell per species (with four species: background and CS electrons and ions) in 2D, whereas, in 3D, 10 macroparticles/cell/species sufficed.

No initial perturbation is used to kickstart reconnection, because such a perturbation (if uniform in z) can significantly suppress 3D effects (Werner & Uzdensky 2021). Initial instabilities are therefore seeded by macroparticle noise.

Over time, transverse magnetic energy U_Bxy is released to other forms (U_Bxy excludes energy in guide field B_z , which cannot be released—see Section 4). Figure 1(a) shows the evolution of U_Bxy (t) for selected simulations. Figure 1(b) shows the net loss in U_Bxy over T = 20L/c as a function of B_gz , for all simulations (large symbols). Ultimately this energy ΔU_Bxy goes almost entirely to particles (ΔU_ptcl, small symbols; see Section 6), with the small difference ∣ΔU_Bxy ∣ − ΔU_ptcl comprising mainly ΔU_Bz , which is the increase in guide-field energy (see Section 4).

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In 2Dxy (Figure 1(a), blue triangles), magnetic energy decreases rapidly due to magnetic reconnection until saturation after 5–10 L/c. During that time we observe the familiar behavior of plasmoid-dominated reconnection. Reconnection pumps magnetic energy and flux from the upstream into plasmoids (magnetic islands), continually growing the total plasmoid volume and the magnetic energy therein. Apart from merging, plasmoids are permanent (stable) in 2D. Eventually (after 5–10 L/c), in a closed system, the largest plasmoid becomes so large (∼L) that it halts reconnection—even though considerable transverse magnetic energy may remain upstream as well as in the plasmoid.

In 2Dyz (Figure 1, red diamonds), tearing and reconnection are forbidden, but the nonlinear DKI can rapidly release magnetic energy. We observe qualitatively similar behavior—the rippling of the CS, sometimes leading to a catastrophic folding over on itself—as reported in nonrelativistic electron–ion plasma with artificially low m_i /m_e and in relativistic pair plasma (Ozaki et al. 1996; Pritchett & Coroniti 1996; Pritchett et al. 1996; Zhu & Winglee 1996; Zenitani & Hoshino 2007; Cerutti et al. 2014; Werner & Uzdensky 2021). The nonlinear DKI effectively thickens the CS, significantly slowing but not fully halting energy conversion. A DKI mode may enter the nonlinear stage when its rippling amplitude exceeds its rippling wavelength, but—like waves breaking in the ocean—whether and where this occurs has a substantial element of randomness (see Figures 28, 29, and 35 in Werner & Uzdensky 2021). While a large statistical study is beyond the scope of this work, this stochastic variation is shown via the three 2Dyz simulations with B_gz = 0 (red diamonds and thin dashed lines) in Figure 1(a).

In 3D (Figure 1, magenta circles), U_Bxy can be released by reconnection and DKI. In addition, flux ropes (3D plasmoids) formed by reconnection may decay via the flux-rope kink instability, releasing still more magnetic energy than in 2D (Figure 1(b)). Because kinking flux ropes decay, reconnection will not halt as in 2Dxy, although CS thickening (due to DKI and flux-rope instability) slows both DKI and reconnection; all the 3D simulations in Figure 1(a) show continued but slow energy conversion beyond 20 L/c (Werner & Uzdensky 2021).

In Figure 1(b) we see that, for B_gz = 0, all dimensionalities yield comparable ∣ΔU_Bxy ∣ ∼ 0.2–0.3U_Bxy0. While a small guide field B_gz /B₀ = 1/4 has only a small effect in 2Dxy and 3D, it strongly inhibits energy conversion in 2Dyz (Zenitani & Hoshino 2008).

Increasing B_gz has two main effects, in all cases: it slows energy conversion, and decreases the net magnetic energy release ∣ΔU_Bxy ∣. A guide field of B_gz /B₀ ≳ 1/2 stabilizes the DKI in 2Dyz (see Zenitani & Hoshino 2008; Schoeffler et al. 2023), preventing any release of U_Bxy . For 2Dxy and 3D, increasing B_gz /B₀ from 0 to 1 slows energy conversion and reduces ∣ΔU_Bxy ∣ by roughly half; by B_gz /B₀ = 2, only about 0.1U_Bxy0 is released (this depends on the aspect ratio: for L_y ≳ L_x , we expect ∣ΔU_Bxy ∣/U_Bxy0 ∼ 0.1L_x /L_y ). Previous 2Dxy studies showed that B_gz slows reconnection by reducing the Alfvén speed v_A,x in the outflow direction (Liu et al. 2014; Werner & Uzdensky 2017); also, B_gz resists plasmoid compression, halting reconnection at smaller ∣ΔU_Bxy ∣. These trends hold in 3D as well, except that increasing B_gz /B₀ from 0 to 1/4 releases more energy, possibly because B_z suppresses the DKI and prevents interference with reconnection, or possibly this is stochastic variation; we leave exploration of this subtrend to future work.

Overall, after 20 L/c, ΔU_Bxy is about 15% higher in 3D than in 2Dxy because 3D evolution accesses all the 2D dissipation channels plus the flux-rope instability; the difference between 2Dxy and 3D narrows slightly with higher B_gz as guide field increases uniformity in z. We note that with more time, ∣ΔU_Bxy ∣ would increase in 3D, but not in 2Dxy.

In our simulations, the guide-field energy U_Bz can only increase from its initial value; the B_z -flux through any x–y plane is conserved and B_z is initially uniform, yielding the lowest U_Bz for the fixed flux. Figure 2(a) shows the net gain ΔU_Bz versus B_gz for each dimensionality. In the 2Dyz case, ΔU_Bz ≈ 0, and for B_gz = 0 neither 2Dxy nor 3D show noticeable gain. However, for B_gz > 0, reconnection outflows compress plasma and guide field in flux ropes, increasing U_Bz . The gain ΔU_Bz increases with B_gz /B₀ ≲ 0.5 because there is more B_z to be compressed; however, stronger B_gz rivals the plasma in resisting compression (with adiabatic index 2, greater than the adiabatic index 4/3 or 5/3 of relativistic or nonrelativistic plasma; see Section 4.4 of Werner & Uzdensky 2021), and ΔU_Bz peaks around 0.04 U_Bxy0 at B_gz /B₀ ∼ 0.5 before decreasing. The similarity between 2Dxy and 3D suggests reconnection occurs to similar extents—though slower in 3D—resulting in similar compression of flux ropes, with energy remaining in U_Bz even as flux ropes decay in 3D.

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We note that the contribution of the Hall quadrupole B_z field is negligible on global energy scales, because it is localized to small regions around X-lines; in contrast, the U_Bz in plasmoids becomes globally significant because it grows with plasmoids, which approach the system size.

The net gain in electric field energy U_E is negligible in all cases—less than 0.004 U_Bxy0 (Figure 2(b)). For 2Dyz and 3D, U_E (t) is small at all times. However (see Figure 2(c)), in 2Dxy with strong guide field, U_E (t) builds up substantially over time before declining (after most reconnection has occurred); this effect increases with B_gz . For B_gz /B₀ = 2, 17% of the ultimately released magnetic energy resided at one time (around t = 5L/c) in U_E , and for B_gz /B₀ = 4, over 30%.

This effect—by which substantial U_Bxy is first converted to U_E before energizing particles—has not been reported before, to our knowledge. We find that (when B_gz /B₀ ≳ 0.5) U_E is dominated by E_y in plasmoids; this is simply the motional electric field E_m,y ≈ v_x B_z /c due to B_z in a plasmoid moving with relativistic speed v_x along the layer. This effect should appear in any 2D reconnection simulation with guide field and relativistic outflows, even in pair plasma. After the last major plasmoid merger, as reconnection is ending, only one large but stationary plasmoid remains, and thus the motional electric field ultimately decays.

We can estimate how E_m,y ≈ v_x B_z /c scales with guide field, assuming that B_z ∼ B_gz and that plasmoid velocity v_x scales with v_A,x , the Alfvén velocity projected along x. Since the typical reconnection electric field is E_rec ∼ 0.1v_A,x B₀/c (for fast collisionless reconnection), E_m,y /E_rec ∼ 10B_gz /B₀, which exceeds unity for even small B_gz . In absolute terms, ${v}_{A,x}=c{[{B}_{0}^{2}/(4\pi h+{B}_{0}^{2}+{B}_{{gz}}^{2})]}^{1/2}$, where h is the relativistic plasma enthalpy density including rest mass (Liu et al. 2014; Sironi et al. 2016; Werner & Uzdensky 2017), and thus

$$\begin{eqnarray}\begin{array}{rcl}{E}_{m,y}({B}_{{gz}}) & \sim & \sqrt{\displaystyle \frac{{B}_{{gz}}^{2}{B}_{0}^{2}}{4\pi h+{B}_{0}^{2}+{B}_{{gz}}^{2}}}\\ & \to & \left\{\begin{array}{ll}{E}_{m,y}\propto {B}_{{gz}} & {B}_{{gz}}^{2}\ll {B}_{0}^{2}+4\pi h\\ {E}_{m,y}\sim {B}_{0} & {B}_{{gz}}^{2}\gtrsim {B}_{0}^{2}+4\pi h\end{array}\right..\end{array}\end{eqnarray} \tag{ 1 }$$

(In this paper, $4\pi h\approx 4\pi {n}_{b}{m}_{i}{c}^{2}={B}_{0}^{2}/{\sigma }_{i}=2{B}_{0}^{2}$.)

This estimate of E_m,y (B_gz ) roughly explains the B_gz -dependence of E_y in our 2Dxy simulations; Figure 2(d) shows the maximum observed E_y compared with

$$\begin{eqnarray}&&{E}_{y,\max }({B}_{{gz}})=\sqrt{{E}_{y0}^{2}+{[\alpha {E}_{m,y}({B}_{{gz}})]}^{2}},\end{eqnarray} \tag{ 2 }$$

which adds in quadrature the motional field E_m,y (B_gz ) given by Equation (1) and ${E}_{y0}\equiv {E}_{y,\max }(0)\approx 0.14{B}_{0}$, an estimate of E_y from other sources (which we measure in the simulation with B_gz = 0 and assume it remains similar for B_gz > 0), with empirical factor α ≈ 0.6 accounting for, e.g., v_x < v_A,x .

Notably, when U_E dissipates at the end of reconnection, it preferentially energizes electrons, as described next.

In all dimensionalities, increasing guide field generally suppresses both electron and ion energization relative to the available magnetic energy U_Bxy0 (Figures 3(a), (b)). In 2Dyz, both electron and ion net gains (ΔU_e and ΔU_i ) drop precipitously with B_gz . In 2Dxy and 3D, energy gains also fall, but not to zero, and ΔU_i falls much faster than ΔU_e . As B_gz /B₀ increases from 0.25 to 2, ΔU_e falls from 0.09U_Bxy0 to 0.05U_Bxy0 in 2Dxy, and from 0.16U_Bxy0 to 0.09U_Bxy0 in 3D; in contrast, ΔU_i falls from about 0.17U_Bxy0 to just 0.02U_Bxy0 (almost an order of magnitude!), and is nearly identical in 2Dxy and 3D. The additional magnetic energy released in 3D (compared with 2Dxy) goes mostly to electrons. At low B_gz , this may be due to the DKI and/or the flux-rope kink instability; at higher B_gz , DKI is quenched, suggesting that the flux-rope kink preferentially energizes electrons. The electron energy gain fraction q_e ≡ ΔU_e /(ΔU_e + ΔU_i ) grows with B_gz (Figure 3(c)), even though ΔU_e decreases. In 2Dxy, q_e ≈ 0.35 at B_gz = 0, increasing to q_e ≈ 0.5 (equipartition) around B_gz /B₀ = 0.75, and reaching q_e > 0.8 by B_gz /B₀ = 4. In 3D, q_e (B_gz ) is higher than in 2Dxy by about 0.1 (though this gap narrows as B_gz increases), reaching equipartition near B_gz /B₀ = 0.25, and q_e ≈ 0.7 at B_gz /B₀ = 1. In 2Dyz, q_e is ∼0.2 higher than in 3D, but we emphasize that, for B_gz /B₀ ≥ 0.5, ΔU_e in 2Dyz is tiny compared with 2Dxy and 3D (hence hard to measure).

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The 3D case with B_gz = 0 is exceptional, converting less energy than higher B_gz /B₀ = 0.25, but the difference is within the stochastic variation observed in 2Dyz for B_gz = 0 (see Figures 1(b) and 3(a), (b)).

In the following, we compare q_e previously measured in 2Dxy PIC reconnection simulations in the (nearly) semirelativistic, plasmoid-dominated regime. For B_gz = 0, q_e ≃ 0.25–0.35 was found in similar simulations (Rowan et al. 2017; Werner et al. 2018; Rowan et al. 2019; Zhang et al. 2021b) and also in the different regime of nonrelativistic laboratory experiment (e.g., Yamada et al. 2014). Similar increases in q_e with B_gz were also reported in 2D: e.g., Rowan et al. (2019) found q_e increasing to equipartition around B_gz /B₀ ≈ 1 and up to 0.92 for B_gz /B₀ = 6; with reduced mass ratio μ = 25, Melzani et al. (2014b) found q_e increasing to 0.67 at B_gz /B₀ = 1. There have, however, been no 3D PIC simulations in a quantitatively comparable regime (to our knowledge) that have measured q_e .

Although a detailed analysis of energization mechanisms is beyond the scope of this Letter, the time dependence of q_e offers some insight. Figure 3(d) plots q_e separately for each third (in terms of ΔU_Bxy , not time) of each simulation. In 2Dyz, we observe no significant time dependence of q_e . For 2Dxy and strong B_gz , however, the last third (when U_E dissipates; see Figure 2(c)) has much higher q_e than the first two-thirds. Therefore, we conclude that energization by the motional electric field E_m,y differs from reconnection energization mechanisms that operate earlier (or without B_gz ), and yields higher q_e . In 3D, for strong B_gz , we see the last two-thirds have higher q_e than the first third, suggesting that U_E builds up a little in 3D, but is promptly dissipated. That is, energization via E_m,y operates continuously throughout 3D reconnection, but only at the end of 2Dxy reconnection due to the high integrity of plasmoids. Besides being useful in their own right, measurements of q_e can thus help distinguish between different energization mechanisms.

Using PIC simulation, we evolve a thin CS in 3D semirelativistic plasma (see Table 1), investigating energy conversion for different guide magnetic fields B_gz . The 3D simulations are compared with 2Dxy (reconnection) and 2Dyz (drift-kink) simulations with the same initial conditions.

We quantify the net changes in transverse and guide magnetic, electric, electron kinetic, and ion kinetic energies. We find the following:

• 1.  
  Increasing B_gz slows energy conversion and reduces the total released magnetic energy.
• 2.  
  Increasing B_gz suppresses ion energization more than electron energization, increasing q_e ≡ ΔU_e /(ΔU_e + ΔU_i ). In 3D, ΔU_e /U_Bxy0 falls from 0.16 to 0.09 as B_gz /B₀ increases from 0.25 to 2, while ΔU_i /U_Bxy0 falls from 0.17 to 0.02; q_e rises from roughly 0.5 to 0.8.
• 3.  
  In 3D only, the flux-rope kink instability further energizes particles (mostly electrons), releasing the reconnected transverse magnetic energy stored in flux ropes, but not their guide-field energy (which is increased by compression during reconnection).
• 4.  
  Relativistic reconnection in strong guide field transfers energy to transient motional electric fields E_m,y in flux ropes before preferentially energizing electrons. In 2Dxy, U_E grows substantially, and dissipates only at the end of reconnection; in 3D, U_E dissipates promptly, possibly due to flux-rope decay.
• 5.  
  Different plasma processes operating in thin CSs yield different electron/ion energy partitions. We roughly distinguished electron energy fractions q_e due to four mechanisms: DKI, classic 2D reconnection, dissipation of E_m,y , and flux-rope kink instability. Their relative roles (especially for DKI and reconnection) in 3D may be sensitive to the CS configuration.

We have thus characterized the conversion of magnetic energy to electron and ion kinetic energy in 3D CSs, addressing a fundamental plasma-physics question and obtaining new insight into the interplay of multiple dissipation channels yielding different energization of electrons versus ions. Importantly, we measured, from first-principles simulation, electron and ion heating fractions critical for subgrid modeling of electron energization (e.g., Dexter et al. 2020; Scepi et al. 2022), and we showed that they depend significantly on the guide magnetic field. These results, in combination with similar studies in the 3D relativistic pair-plasma regime (e.g., Yin et al. 2008; Zenitani & Hoshino 2008; Liu et al. 2011; Kagan et al. 2013; Cerutti et al. 2014; Guo et al. 2014, 2021; Sironi & Spitkovsky 2014; Werner & Uzdensky 2017; Zhang et al. 2021a; Werner & Uzdensky 2021), will be important in connecting magnetic energy dissipation with particle energization and observed radiation in the complex and varied enviroment of accreting BHs.

This work was supported by NSF grants AST-1806084 and AST-1903335 and by NASA grants 80NSSC20K0545 and 80NSSC22K0828. The 3D simulations used computer time provided by the U.S. Department of Energy's (DOE) Innovative and Novel Computational Impact on Theory and Experiment (INCITE) Program, and in particular used resources from the Argonne Leadership Computing Facility, a U.S. DOE Office of Science user facility at Argonne National Laboratory, which is supported by the Office of Science of the U.S. DOE under Contract No. DE-AC02-06CH11357. The 2D simulations were run on the Frontera supercomputer at the Texas Advanced Computing Center (TACC) at The University of Texas at Austin.