Dynamics and Confinement Characteristics of the Last Closed Surface in a Levitated Dipole Configuration

Abstract

Based on the magnetic configuration of the China Astro-Torus-1 (CAT-1) levitated dipole device, this study investigated the confinement performance of common discharge gas ions under E × B transverse transport conditions induced by electric fields. By adjusting L-coil parameters to shift the inject location, it was found that when the loss boundary is in the outer weak-field region, most particles with large Larmor radii are lost after colliding with the wall, for particles with large pitch angles, the strongly anisotropic magnetic field causes particles across a broad range of energies to be lost through the X-point into the divertor. The study demonstrates that for particle kinetic energies between 100 and 300 eV, the CAT-1 device exhibits a loss cone angle θ_loss of approximately 58°, indicating favorable confinement performance.

1. Introduction

In cosmic space, plasma confinement by dipole fields is a prevalent phenomenon observed in stellar and planetary magnetospheres [1]. Studies on magnetically confined plasmas in space dipole fields have revealed high-beta plasmas and compressibility phenomena. Hasegawa et al. proposed the concept of a D-He³ fusion reactor based on dipole field configurations and pioneered the use of superconducting levitated dipole coils to generate dipole magnetic fields [2,3]. Experimental facilities in this domain include the Levitated Dipole Experiment (LDX) and Ring Trap-1 (RT-1), both employing superconducting magnetic levitation technology. Notably, the LDX first observed inward density pinch effects during levitation experiments [4] and demonstrated stable plasma confinement under high-beta conditions [5,6,7]. The RT-1 device first achieved a local beta value peak exceeding 100% in experiments [8], successfully simulated particle acceleration in planetary radiation belts [9], and spontaneously excited and nonlinearly evolved whistler waves in a dipole magnetic field for the first time [10]. These experiments have validated the feasibility of the dipole magnetic field–confined fusion concept, offering a foundation for further research. China is now developing the SPERF system, mainly for space physics research [11], and designing the China Astro-Torus 1 (CAT-1) device for fusion energy research [12].

In levitated dipole devices, the dipole coil (D-coil) is magnetically suspended by the attractive force provided by the levitated coil (L-coil) positioned above the vacuum chamber. Due to the co-directional currents in both coils, an X-point separatrix forms between the D-coil and L-coil, thereby separating the confined plasma region from the external vacuum region. Radial particle transport has been experimentally observed in both the LDX and RT-1 devices [4,10]. The underlying mechanism for this outward transport is a turbulence reversal process triggered by the breakdown of self-organized equilibrium: The injection of neutral gas cools the hot electrons, leading to a flattening of the peaked density profile (thus disrupting self-organized equilibrium) and exciting low-frequency entropy-mode turbulence (~1 kHz). This turbulence drives an outward E×B drift. Concurrently, turbulent magnetic fluctuations (reaching 3–4% of the equilibrium field) distort the edge magnetic field lines. Combined with the open magnetic field line topology, this accelerates particle escape along the magnetic field gradient towards the vacuum chamber wall. The process of particle loss along open magnetic field lines in a levitated dipole configuration is analogous to the precipitation of energetic particles along Earth’s dipole field lines into the polar atmosphere, which generates the aurora. Particle simulation studies indicate that auroral generation in the magnetosphere primarily relies on two mechanisms: (1) wave–particle resonant scattering of electron pitch angles to populate the loss cone and (2) the lowering of mirror points deep into the atmosphere, leading to collisional destruction of the magnetic moment. Additionally, the particle kinetic energy must exceed a specific threshold [13,14,15]. For laboratory magnetic confinement devices, simulation studies of particle behavior near the separatrix are crucial for optimizing confinement performance and engineering design. Analyzing particle trajectories resulting from drifts, collisions, and magnetic topology effects provides a theoretical basis for enhancing confinement efficiency [16,17,18,19]. Furthermore, utilizing trajectory simulations to predict divertor heat load distributions and material erosion hotspots guides the optimization of magnetic configurations, such as divertor design [20,21].

Based on the above, in levitated dipole configurations, turbulence reversal triggered by the breakdown of self-organized equilibrium drives the outward radial transport of particles. When particles reach the separatrix of the levitated dipole field, they are lost along open magnetic field lines. Studying particle trajectories near the separatrix not only directly reflects the confinement characteristics of the levitated dipole field for particles but also provides critical guidance for assessing the heat load of escaping ions on the vacuum chamber wall. Furthermore, it offers valuable insights into the analogous mechanisms underlying auroral phenomena in the Earth’s magnetosphere. This study employs a test–particle simulation approach. Utilizing the magnetic field configuration parameters of the CAT-1 device, we statistically analyzed the loss cone distribution characteristics of common discharge gas ions (H⁺, D⁺, and T⁺). Additionally, we computed their characteristic transit times and characteristic transit distances, thereby providing an intuitive assessment of the device’s confinement performance. The paper is structured as follows: Section 2 introduces the magnetic field configuration of the CAT-1 device and the test–particle simulation methodology. Section 3 analyzes the loss cone characteristics and loss behavior of different ions near the separatrix. Finally, a summary of the research is presented.

2. Research Methods

2.1. Levitated Dipole Magnetic Configuration

In the Cartesian coordinate system, the magnetic field B produced by multiple coils in space is obtained through the vector superposition of the magnetic fields generated by individual coils. The magnetic field B can be calculated by taking the curl of the azimuthal component of the magnetic vector potential, ${\mathit{A}}_{\mathit{\varphi }}$. The expressions for the magnetic vector potential ${\mathit{A}}_{\mathit{\varphi }}$ and the magnetic flux ψ at an arbitrary point in space are given as follows [22]:

$${\mathit{A}}_{\varphi }=\sum _{i=1}^n{\displaystyle \frac{{\mu }_0{I}_i{a}_i}{\pi \sqrt{{\left(a_i+R\right)}^2+{\left(Z-Z_i\right)}^2}}}\left[{\displaystyle \frac{\left(2-k_i^2\right)K\left(k_i\right)-2E\left(k_i\right)}{k_i^2}}\right]{\mathit{e}}_{\varphi },$$

(1)

$${\psi }_{\varphi }=-R{A}_{\varphi }=-\sum _{i=1}^n{\displaystyle \frac{{\mu }_0{I}_i{a}_{i}R}{\pi \sqrt{{\left(a_i+R\right)}^2+{\left(Z-Z_i\right)}^2}}}\left[{\displaystyle \frac{\left(2-k_i^2\right)K\left(k_i\right)-2E\left(k_i\right)}{k_i^2}}\right].$$

(2)

$$k_i^2={\displaystyle \frac{4a_{i}R}{{\left(a_i+R\right)}^2+{\left(Z-Z_i\right)}^2}}.$$

(3)

where ${\mu }_0$ is the vacuum permeability; n denotes the number of coil turns; $I_i$, $R_i$, and $Z_i$ represent the current, radial coordinate, and axial coordinate of the i-th circular current loop, respectively; R and Z are the radial and axial coordinates of the observation point; and K and E denote the complete elliptic integrals of the first and second kind, respectively. For a dipole magnetic field, the magnetic vector potential ${\mathit{A}}_{\mathit{\varphi }}$ possesses only an azimuthal component, while the azimuthal component of the magnetic field is zero. The other two components are given as follows [22]:

$$B_R=\sum _{i=1}^n{\displaystyle \frac{-{\mu }_0{I}_i\left(Z-Z_i\right)}{2\pi R\sqrt{{\left(a_i+R\right)}^2+{\left(Z-Z_i\right)}^2}}}\left[K\left(k_i\right)-{\displaystyle \frac{a_i^2+R^2+{\left(Z-Z_i\right)}^2}{{\left(a_i-R\right)}^2+{\left(Z-Z_i\right)}^2}}E\left(k_i\right)\right],$$

(4)

$$B_Z=\sum _{i=1}^n{\displaystyle \frac{{\mu }_0{I}_i}{2\pi \sqrt{{\left(a_i+R\right)}^2+{\left(Z-Z_i\right)}^2}}}\left[K\left(k_i\right)+{\displaystyle \frac{a_i^2-R^2-{\left(Z-Z_i\right)}^2}{{\left(a_i-R\right)}^2+{\left(Z-Z_i\right)}^2}}E\left(k_i\right)\right].$$

(5)

Since this study focuses on particle confinement characteristics at the last closed flux surface (LCFS)—which resides on the equipotential surface of magnetic null points (X-points)—the X-point locations are determined by solving the condition ∇ψ = 0. Given the toroidally symmetric configuration of the levitated dipole field, the X-point search can be confined to the R-Z poloidal plane using the Newton–Raphson iterative method [23]. The governing equations are expressed as follows:

$$\left[\begin{array}{c}{R}^{n+1}\\ Z^{n+1}\end{array}\right]=\left[\begin{array}{c}{R}^n\\ Z^n\end{array}\right]+{\displaystyle \frac{1}{\mathit{det}\left(H\right)}}{H}^{*}·\left[\begin{array}{c}{\psi }_R\\ {\psi }_Z\end{array}\right].$$

(6)

where R and Z denote the radial and axial coordinates, respectively, with superscripts and n+1 indicating the n-th and (n + 1)-th iterations. ψ_R and ψ_Z represent the partial derivatives of the magnetic flux ψ with respect to R and Z, and H is the Hessian matrix.

Under the CAT-1 parameters, magnetic field lines are traced using the field line equation [24], denoted as dR/B_R = dZ/B_Z = ds/|B|. The D-coil has a radius R_DC = 0.5 m, is positioned at height Z_DC = 0 m, and carries a current I_DC = 4.77 MA. The L-coil has a radius R_LC = 0.85 m, is positioned at height Z_LC = 2.1 m, and carries a current I_LC = 0.56 MA.

Figure 1a shows a schematic of magnetic field lines plotted using the fourth-order Runge–Kutta method. The X-point is located at R = 1.42 m, Z = 1.62 m. The separatrix intersects the plane Z = 0 m at R = 2.86 m.

Figure 1b presents a two-dimensional contour plot of the magnetic field strength distribution for the CAT-1 model. The maximum magnetic field strength, approximately 12 T, occurs near the inner side of the coils. The field strength decays rapidly with increasing radial distance R, scaling approximately as |B| ∝ 1/R³.

2.2. Equations of Motion Under Lorentz Force Dynamics

The motion of charged particles in electromagnetic fields is governed by the Lorentz force equation [25]:

$${\displaystyle \frac{d\mathit{v}}{dt}}={\displaystyle \frac{q}{m}}\left(\mathit{E}+\mathit{v}\times \mathit{B}\right).$$

(7)

where v is the velocity vector, q and m denote the particle charge and mass, and E and B are the electric and magnetic field vectors, respectively.

This study employed the Boris algorithm [26,27] to compute particle trajectories, a method renowned for its long-term energy conservation properties. The discretized form of Equation (7) is structured as follows:

$${\mathit{v}}_{k+1}=R{\mathit{v}}_k+{\left(I+{\Omega }_k\right)}^{-1}{\displaystyle \frac{q}{m}}\mathrm{d}t{\mathit{E}}_k,$$

(8)

$${\mathit{x}}_{k+1}={\mathit{x}}_k+R{\mathit{v}}_k\Delta t+{\left(I+{\Omega }_k\right)}^{-1}{\displaystyle \frac{q}{m}}\mathrm{d}{t}^2{\mathit{E}}_k,$$

(9)

$$R={\left(I+{\Omega }_k\right)}^{-1}\left(I-{\Omega }_k\right),$$

(10)

$${\Omega }_k={\displaystyle \frac{q}{m}}\left[\begin{array}{ccc}0& -B_3\left(x_k\right)& B_2\left(x_k\right)\\ B_3\left(x_k\right)& 0& B_1\left(x_k\right)\\ -B_2\left(x_k\right)& -B_1\left(x_k\right)& 0\end{array}\right]\mathrm{d}t.$$

(11)

where v, x, and E denote the velocity, position, and electric field vectors, respectively. Δt is the time step, with subscript k indicating quantities at the k-th time step. I represents the 3 × 3 identity matrix, and B₁, B₂, and B₃ correspond to the Cartesian components of the magnetic field B.

Particle trajectories can be obtained by iterating Equations (8) and (9). The coefficient matrix Ω_k in Equations (10) and (11) is determined at the k-th time step using Equations (4) and (5).

Figure 2 compares the evolution of normalized kinetic energy over time for a charged particle undergoing gradient drift motion, simulated using the Boris algorithm and a seventh-order fixed-step Runge–Kutta algorithm. The results demonstrate that the Boris algorithm exhibits excellent energy conservation properties. In this work, the particle kinetic energy range was calculated using the ideal scaling relation [11]. This scaling is applied between the characteristic length, characteristic density, and characteristic magnetic field strength of the RT-1 device [28,29] and the corresponding parameters in CAT-1 [12]. Using this ideal MHD scaling relation yields an ion temperature range for CAT-1 of T_i ≈ 100∼300 eV.

3. Results and Discussion

3.1. Particle Dynamics at LCFS

In this study, H⁺, D⁺, T, and He²⁺ were selected as test particles as they cover fusion fuels, products, and key impurities. Their differing charge-to-mass ratios can comprehensively verify the universality of magnetic field confinement and particle dynamics. The masses, charges, and particle mass ratios of the four charged particles are listed in

Table 1. Mass and ratio of charge and mass for alpha, hydrogen, and its isotope ions [30].

	m (kg)	q/m (C/kg)
H+	1.6 × 10−27	9.6 × 107
D+	3.3 × 10−27	4.8 × 107
T+	5.0 × 10−27	3.2 × 107
He2+	6.6 × 10−27	4.8 × 107

. Particles constrained in a dipole field typically satisfy three adiabatic invariants: magnetic moment adiabatic invariant $\mu$, longitudinal adiabatic invariant $J$, and flux adiabatic invariant $\psi$. These correspond to gyrating motion perpendicular to the magnetic field, bouncing motion parallel to the magnetic field, and drifting motion along the toroidal direction. The presence of these invariants allows particles to be confined in a dipole field long-term. For particles with kinetic energy of 100–300 eV, adiabatic invariants are broken when their orbits pass through the X point. Whether particles pass through the X point depends on their initial kinetic energy and pitch angle. Note that the superposition of the levitated coil magnetic field causes the configuration to lose upper–lower symmetry, necessitating a correction to the pitch-angle parameter. The numerical simulation time step is Δt = 1 × 10⁻⁹ s. For H⁺, D⁺, T⁺, and He²⁺ particles with initial pitch angles of 60° and 30°, the initial kinetic energy is 200 eV, starting at the mid-plane $R$ = 2.86 m. Figure 3 shows the trajectories of the four types of particles and the time evolution curves of the normalized magnetic moment $\mu$.

Figure 3a shows the projection trajectory of particles with an initial pitch angle of 60°. Due to the small initial parallel velocity component, particles return to the equator due to the magnetic mirror effect before reaching the X point, exhibiting cyclotron-bounce motion along the magnetic field lines, thus achieving long-term confinement. Figure 3b shows the normalized magnetic moment $\mu =\mu /<\mu >$ (where <⋯> denotes time averaging) of the particles. The four types of particles have different oscillation amplitudes and periods of magnetic moments due to the differences in Larmor radius and charge-to-mass ratio. However, the average value of the magnetic moment of the same type of particles is constant within the cyclotron period, confirming the adiabatic invariance of the magnetic moment. Notably, the superposition of the levitated coil magnetic field breaks the upper–lower symmetry of the pure dipole field, causing the magnetic moment period to be restructured into the bounce period of particles traveling from the equator through the polar region and back to the equator.

Figure 3c shows the projection trajectory of particles with a pitch angle of 30°. As the parallel velocity increases, the magnetic mirror points move towards the X point; when the magnetic mirror points surpass the X point, particles exhibit two types of orbits: (1) reflecting back in the dipole field after passing through the X point and (2) being captured by the levitated coil magnetic field and then returning to the dipole field. Figure 3d shows the magnetic moment evolution of the two types of orbits: the former has an “M”-shaped oscillation in the normalized magnetic moment due to two traversals through the X point vicinity; the latter experiences non-periodic magnetic moment disturbances when passing through the X point. The magnetic moments of both types of trajectories lose their periodic evolution patterns.

3.2. Particle Confinement Time and Trajectory Length at the LCFS

The previous research shows that under the same initial kinetic energy and position conditions, particle trajectories are highly dependent on the pitch angle. Observations show that some particles, after crossing the X point, return to the dipole field temporarily, but after several bounce periods, they are still gradually captured by the levitated coil magnetic field. To quantify this process, the flight time (from release to when the particle exceeds the vacuum chamber boundary) and flight length (trajectory distance) along the magnetic separatrix were defined. For the four particle types (H⁺, D⁺, T⁺, and He²⁺, isotropic pitch angles, 18,000 samples total), to improve computational efficiency, the pitch-angle range was set to 0–70° due to the sustained confinement of large-pitch-angle particles. Figure 3 plots the evolution of normalized particle flux versus flight time and flight length.

Figure 4a shows the evolution of normalized confined particle flux with flight time. It reveals that about 80% of particles crossing the magnetic separatrix are lost within 0.6 ms, regardless of ion species. Note that the current assessment of the confined fraction is relatively conservative. When considering the full pitch-angle range of 0–90° (with a smaller number of test particles), the confined fraction can increase to 36%. Figure 4b plots the evolution of normalized confined particle flux with flight distance. H⁺ exhibits the greatest flight distance of about 36 m. This is because, at the same kinetic energy, H⁺ and He²⁺ have similar orbits. However, particle velocity satisfies $v\propto 1/\sqrt{m}$, so $v_H$ > $v_{He}$. Thus, H⁺ reaches the ion loss flux threshold earlier, resulting in a shorter flight time compared to He²⁺.

Table 2. Averaged values of flight times and lengths for all kinds of particles.

	H+	D+	T+	He2+
Particle Flight Time (ms)	0.185	0.190	0.205	0.263
Particle Flight Length (m)	36.3	26.5	23.2	25.8

lists the average flight time and average flight distance for all particles.

3.3. The Impact of Levitated Coil Parameters on the Loss Cone

In a levitated dipole field configuration, the dipole field coil is suspended by the magnetic field from a levitation coil at the top of the vacuum chamber, forming a magnetic separatrix structure with an X point. By adjusting the parameters of the L-coil, the position of the magnetic null point can be tuned, thus controlling the position of the boundary line on the mid-plane and effectively managing the injection point location.

To evaluate the particle confinement in the CAT-1 device, this study focuses on how the L-coil parameters affect the loss cone boundary within the typical ion temperature range. Although H⁺ and He²⁺ trajectories are similar at the same kinetic energy, they differ in latitude amplitude. To balance computational efficiency and time resolution, H⁺, D⁺, and T⁺ were chosen as representative particles (He²⁺ behavior can be inferred). From Section 3.2, most particles are lost within 0.6 ms, so the calculation time was set to 0.6 ms. Particles were assumed to be injected isotropically with an angle resolution of $\delta \theta$ = 0.1°. The L-coil parameters varied as follows: levitation coil current $I_{LC}$ = 0.25–0.75 MA; levitation coil radius $R_{LC}$ = 0.65–0.95 m; and levitation coil height $H_{LC}$ = 1.5–2.5 m.

Figure 5a shows the relationship between L-coil parameters and the X-point position, with the horizontal and vertical coordinates normalized to the L-coil radius and height, respectively. The X-point radial position increases with $I_{LC}$, while $R_{LC}$ and $I_{LC}$ increases decrease the radial and vertical positions. Figure 5b shows the trends in the injection point radial position and the corrected angle (the angle between the magnetic field line and the Z-axis) on the mid-plane with varying L-coil parameters. The results indicate that as $H_{LC}$ increases, the injection point radial position increases, moving the injection point away from the weak-field region of the D-coil, with the corrected angle remaining almost unchanged. In contrast, as $I_{LC}$ or $R_{LC}$ increases, the injection point radial position decreases, bringing the injection point closer to the strong-field region of the D-coil, and the corrected angle gradually increases.

To discuss the influence of L coil parameters on the loss cone of particles with different kinetic energies, we assume that the L coil parameters and particle kinetic energy distribution are on a 32 × 32 grid. The particle loss channel is defined as the longitudinal position being higher than the X point’s Y-coordinate by 0.15 m.

Figure 6a–c show the contour plots of the L coil radius versus particle energy for the loss cone of three types of particles. As the L coil radius increases, the injection point moves from a weak-field region to a strong-field region (in the equatorial plane, in the radially inward direction). When the levitated coil radius R_LC exceeds 0.9 m, the loss cone increases rapidly with R_LC. At R_LC = 0.95 m, due to the strong anisotropic magnetic field at the injection point and the gradient and curvature drift effects of the particles, the loss cone for all kinetic energy particles reaches 90°. When the L coil radius is small, the injection point is in a region of weak magnetic field strength. As the injection angle increases, when particles move along magnetic field lines to high-latitude positions, even if they do not pass through the X point and are lost, the increase in Larmor radius causes them to collide with the vacuum chamber and be lost. Moreover, the larger the Larmor radius of the lost particles, the more pronounced this effect becomes. Figure 6d shows the variation in the ratio of the maximum longitudinal position of particle orbits to the limiter height with particle kinetic energy under the conditions of R_LC = 0.65 m, H_LC = 2.1 m, I_LC = 0.56 MA, and an injection angle of 35°. Observing the particle orbits in the R-Z plane, it is found that almost all particles are lost due to collisions with the vacuum chamber wall. The maximum Y-coordinate of the particles increases with particle kinetic energy, and particles with a larger Larmor radius reach the limiter height at lower kinetic energies.

Figure 6e presents the variation in the maximum trajectory of particles with kinetic energy E_K = 240 eV and an injection angle of 50° as the L coil radius changes. As R_LC increases, the magnetic field strength at the injection point increases, mitigating losses caused by particle collisions with the vacuum chamber. However, when R_LC continues to increase, it enhances the loss of particles passing through the X point and entering the divertor. Consequently, the loss cone exhibits a trend of first decreasing and then increasing.

Figure 7a–c show the contour plots of the L coil height versus particle energy for the loss cone of particles. As the height of the L coil increases, the injection point moves from a strong-field region to a weak-field side, and the variation trend of the loss cone is opposite to that with the L coil radius. Figure 7d presents the variation in the ratio of the maximum longitudinal position of particle orbits to the height of the separatrix with particle kinetic energy under the conditions of R_LC = 0.85 m, H_LC = 2.5 m, I_LC = 0.56 MA, and an injection angle of 55°. By examining the projection of particle trajectories in the R-Z plane, it is found that particles with low kinetic energy and small Larmor radii precess to higher latitudes along the magnetic field lines compared to those with higher kinetic energy, making them more likely to be lost through the X point. As the kinetic energy increases, the loss cone exhibits an undulating variation, possibly due to the alternating occurrence of particle loss through the X point and collisions with the vacuum chamber wall. Figure 7e shows the variation in the maximum trajectory of particles with kinetic energy E_K = 260 eV and an injection angle of 60° as the height of the L coil changes. Raising the L coil height increases the limiter position, making it less likely for relatively high-energy particles to cause collisions with the divertor.

Figure 8a–c show the loss cone cloud charts of three kinds of particles with different L-coil currents. The change in current affects the loss cone in a way similar to the change in L-coil radius. But when the L-coil current exceeds 0.7 MA, all particles entering at any injection angle will follow the magnetic field lines into the divertor and be lost. Figure 8d presents a graph showing the ratio of the maximum longitudinal position of the particle orbit to the separatrix height versus particle kinetic energy under the conditions of R_LC = 0.85 m, H_LC = 2.1 m, I_LC = 0.25 MA, and an injection angle of 84°. Low L-coil current causes the LCFS to be very close to the limiter. Even with a large injection angle, high-energy particles with a large Larmor radius tend to collide with the vacuum chamber wall and be lost. Figure 8e shows the variation in the maximum trajectory of particles with kinetic energy E_K = 240 eV and an injection angle of 50° as the L-coil current changes. Similarly, as the L-coil current increases, the loss process shifts from collisions with the vacuum chamber to passing through the X point and entering the divertor.

In a levitated dipole field configuration, varying the L-coil parameters significantly alters the LCFS shape and magnetic field distribution, impacting particle confinement. When L-coil parameters position the particle injection point on the strong-field side, particles launched at large angles can pass through the X point and enter the divertor, causing loss. Conversely, when the injection point is on the weak-field side, most particles are lost due to collisions with the vacuum chamber wall caused by their large Larmor radius, with some low-energy particles lost as a result of moving along field lines to high latitudes. Studies show that for CAT-1, with particle kinetic energy of 100–300 eV, the loss cone ${\theta }_{loss}$ is about 58°, indicating good particle confinement.

4. Conclusions

In summary, this study delves into the dynamics and confinement characteristics of particles within a levitated dipole configuration, leveraging the parameters of the CAT-1 device. The research demonstrates that the CAT-1 device can achieve favorable confinement performance for particles with kinetic energies between 100 and 300 eV, exhibiting a loss cone angle of approximately 58°. This indicates that the majority of particles can be effectively confined within the plasma region. The study also explores the loss behavior of different ions near the last closed flux surface (LCFS) and calculates their characteristic transit times and distances, providing valuable insights into the device’s confinement performance. Furthermore, the research investigated the impact of L-coil parameters on the loss cone boundary. By adjusting these parameters, the position of the magnetic null point can be tuned, thereby effectively controlling the injection point location and the loss cone boundary. This study enhances our understanding of particle confinement mechanisms in levitated dipole fields and offers critical guidance for the optimization of magnetic configurations and the assessment of the heat load on vacuum chamber walls in fusion devices. Additionally, it provides insights into the analogous mechanisms underlying auroral phenomena in the Earth’s magnetosphere.