Magnetized plasmas are ubiquitous in the universe and are a primary focus of astrophysical,1–3 space,4–6 and laboratory7–10 plasma research. In these scenarios, the dynamic behavior of plasmas is closely coupled with the transport processes of magnetic fields, giving rise to various complex explosive phenomena such as solar flares and coronal mass ejections,11,12 geomagnetic storms and auroras,13,14 and astrophysical plasma jets and bow shocks.15,16 The study of magnetized plasma compression has sparked great interest in the scientific community, since it has important applications across a wide range of scales. From small-scale magnetized inertial confinement fusion (ICF) implosions to medium-scale plasma confinement in magnetic confinement fusion (MCF),17–20 and extending to larger-scale solar wind–planetary magnetosphere coupling,21–23 and even to astronomical unit-scale astrophysical outflow collimation,16,24 all involve the compression of magnetized plasmas. When magnetized plasmas are compressed, the magnetic field may experience advection dominated by bulk plasma flows or heat flows, be subject to Ohmic diffusion caused by finite plasma resistivity, or be influenced by the Biermann battery effect and induced currents under specific conditions.25–27 These magnetic transport mechanisms collectively govern the evolution of magnetic fields within plasmas, significantly shaping the hydrodynamical behavior and energy transport mechanisms of the plasmas.17,28 Therefore, gaining insights into the magnetic transport mechanisms during the compression of magnetized plasmas is not only beneficial for advancing our understanding of the distant universe, but also holds essential significance for the success of nuclear fusion energy generation and the development of precise space weather models.

In laboratory plasma research, Nernst advection is one of the most important magnetic transport mechanisms in magnetized plasma experiments. It arises from the coupling between the magnetic field and the electron heat flow, causing the magnetic field to move downward along the temperature gradient.29 This mechanism has particular significance in the context of ICF. During the implosion stagnation phase, simulations show that the Nernst effect moves the self-generated Biermann field from the hot core toward the cold edge. This phenomenon leads to demagnetization of the hot-spot core while establishing a strong magnetic field in the edge region.25,30,31 It becomes more intriguing in magnetized-ICF schemes, where the magnetic field applied to the magnetized hot-spot core and the self-generated Biermann field at the edge of the hot-spot coexist.32 The relative importance of these two magnetic fields can be assessed using the electron Hall parameter ω_eτ_e ∝ T^3/2B/(m^1/2n), which depends on the electron temperature T, density n, and magnetic field strength B. Typically, the temperature at the edge of the hot spot is lower, resulting in a Hall parameter from the Biermann field that is less than 1. Consequently, the Biermann effect is commonly overlooked in relevant magnetized-ICF experiments.19 However, under fusion-relevant plasma conditions, the Biermann magnetic field is expected to exceed 10⁴ T,25,33 which is comparable to or even greater than the applied magnetic field. Meanwhile, the typical plasma parameters at the edge25,34 (n ∼ 10³² m⁻³, T ∼ 10³ eV) yield a Spitzer transverse resistivity η_⊥ ∼ 10⁻⁸ Ω m, and thus the characteristic length scale of the hot spot (∼10⁻⁶ m) gives a magnetic Reynolds number of Re_M ∼ 3. This moderate Re_M emphasizes the importance of magnetic diffusion at the edge and suggests that the Biermann magnetic field may possess the potential to diffuse inward. When such a magnetic field configuration is present during the implosion compression process, it is likely to significantly affect the magnetization and hydrodynamics of the hot-spot core. However, to the best of our knowledge, no previous studies have explored this issue in experiments or theory.

In space physics, the compression of magnetized plasma is a fundamental process in the interaction between solar wind and planetary magnetospheres.22,23 In extreme solar wind conditions, the magnetospheric plasma sandwiched between the magnetopause and the planetary surface undergoes significant compression due to the solar wind ram pressure.35 Magnetic transport plays a dominant role in the coupling between the solar wind and the magnetosphere, which is crucial for generating planetary space weather phenomena such as magnetic storms and substorms.13,14,36 The solar wind typically carries an interplanetary magnetic field (IMF) rotating in the north–south direction. The planetary magnetosphere exhibits varied responses to solar wind events that impact the magnetopause with differing magnetic shear angles.21,37 These responses often manifest as changes in the configuration of the magnetopause, particularly in terms of altitude variations, which are crucial parameters in space physics research.14,22,37 On Earth-like planets, the altitude variations at the dayside magnetopause are influenced by various factors, including the solar wind intensity, dayside magnetic reconnection rate, electromagnetic induction in the planetary core, and magnetic transport in the magnetospheric plasma.21,23 These factors are themselves influenced by the magnetic field configuration on either side of the magnetopause. For instance, the dayside reconnection rate significantly varies with the shear angle of the IMF.38 Additionally, resistive diffusion at the magnetopause boundary can influence the variations in the magnetopause configuration under specific solar wind conditions,37 where the magnetopause current sheet exhibits high resistivity and the magnetic field strength is nearly equal on both sides of the sheet. Therefore, accurately describing the changes in the magnetopause configuration under the influence of the solar wind requires a comprehensive consideration of the various factors mentioned above. However, a significant discrepancy remains between current space observations and theoretical models.21 To gain a more precise understanding of the response of the planetary magnetosphere under extreme solar wind conditions, further experimental research on the compression of magnetized plasma is imperative.

Magnetic transport is intricately linked to energy transport in the magnetized plasma compression. To achieve ignition in ICF as per the Lawson criterion, self-heating must overpower all energy loss mechanisms, notably electron thermal conduction and bremsstrahlung radiation.39 Owing to the effective conduction suppression in the hot-spot core by a strong magnetic field,40 highly compressed magnetic fields are utilized to improve fusion performance in ICF.19 For instance, Chang et al.41,42 demonstrated a 30% increase in fusion yield with the implementation of magnetized ICF. On the contrary, it is generally believed that the suppressive effects of magnetic fields on radiation losses can be disregarded, making radiation the predominant energy loss mechanism in magnetized ICF.17,43 Bremsstrahlung radiation theory indicates that the radiation power P_Br is directly proportional44 to n². It has been reported that variations in magnetic fields can significantly influence the hydrodynamics during magnetized plasma compression, thereby affecting the temperature and density evolution in the plasma core.17 This implies that magnetic transport has the potential to influence the energy loss mechanisms in magnetized ICF. Likewise, the potential correlation between magnetic transport and radiation loss could influence the morphology and propagation dynamics of astrophysical plasma outflows, since radiative cooling plays a crucial role in the collimation of such outflows and the formation of bow shock waves.15,16,24 However, this physical correlation is not yet understood.

This paper presents an experimental study of the magnetic transport and radiation properties during the compression of a magnetized plasma. A magnetized plasma column undergoing radial implosion driven by J × B force is produced by a theta pinch device. The plasma parameters are measured using various diagnostic methods. High-resolution observations reveal that the implosion process progresses through three stages: compression, expansion, and recompression. A detailed study of the magnetic transport mechanism during the first compression stage is conducted. Furthermore, the correlation between magnetic transport and radiation properties is investigated by integrating the results of multiparameter measurements throughout the two compression stages.

Figure 1 illustrates the experimental apparatus employed in this study. The magnetized plasmas were generated using a cylindrically-shaped theta pinch, the fundamental working principle of which is thoroughly detailed in the literature.45 In brief, this theta pinch consisted of a 64 μF capacitor bank, a thyratron switch, and a glass vessel (20 cm in diameter and 34 cm in length) surrounded by a six-turn copper solenoid coil. These components formed a closed RLC circuit with a resonance frequency of 8.0 kHz and an inductance of 5.73 μH. Hydrogen gas was injected into the vessel via two inlets on either side of the vessel. A needle leak valve, integrated with a pumping system, was utilized to precisely control the gas pressure, thereby achieving a pseudo-static gas target for plasma generation. The procedure for generating plasmas in this theta pinch involved several steps. First, the capacitor bank was discharged to provide a transient drive current in the coil encircling the vessel. The current waveform exhibited a typical RLC signal with multiple half-cycles, during which plasmas would be sequentially produced. Next, an azimuthal electric field was induced by a time-varying longitudinal magnetic field B_z. This induced gas breakdown along an azimuthal path at the vessel’s periphery, forming an azimuthal current sheet.46 After several necessary pre-ionization half-cycles, the first implosion commenced through the J_θ × B_z force propelling the current sheet radially inward to ionize and compress all gas particles. This process resulted in the formation of a dense magnetized plasma within the axis region. Finally, as the drive current diminished to zero, the plasma expanded and uniformly distributed across the vessel, and so did the magnetic field due to its freezing in the plasma, marking the completion of the first pinch half-cycle. The subsequent half-cycles of pinches followed the same procedure as the initial one, but notably the pinch medium transitioned from gas to magnetized plasma.

In the experiment conducted, a discharge voltage of 20 kV and a hydrogen gas pressure of 20 Pa were used. The plasma was studied with a number of diagnostics. As shown in Fig. 1, a Rogowski coil was used to record the drive current in the discharge coil. Additionally, a magnetic probe was introduced into the vessel to measure the evolution of the magnetic field at the central axis. Using a quartz jacket of 4 mm diameter, the plasma disturbance due to the probe (1 mm in diameter) was negligible. In a typical theta pinch configuration, the plasma initiates axial (z-direction) jetting from both ends immediately after completing the radial (r-direction) implosion.45 When studying plasma compression, it is essential to eliminate interference from the jet stage. The luminosity resulting from the interaction of the jet with the background medium in the extension tube can serve as a monitoring signal for the end of the implosion process. To perform this monitoring, two fast photodiodes (300–1100 nm) were used to synchronously measure the luminosity in different regions, as shown in Fig. 1. Specifically, the detection angle of photodiode-1 covered the vessel and the right-side extension tube to approximately record the total luminosity. By contrast, photodiode-2 focused solely on the left-side extension tube to monitor the end of the plasma radial phase (or the onset of the axial jetting phase). The measured drive current, magnetic field B, and luminosity are shown in Fig. 2. The luminosity profile demonstrates that plasmas persist across multiple half-cycles (each ∼60 μs), with the first and the strongest pinches occurring during the fourth and fifth half-cycles of the drive current, respectively.

To investigate the process of magnetized plasma compression, further measurements were undertaken. These included diagnostics of electron density and electron temperature, as well as plasma dynamic imaging. This investigation focused primarily on the most intense second half-cycle (240–300 μs) of the pinch. The diagnostics of electron density and temperature were conducted using a spectroscopic method using a time-scanned spectral measurement system consisting of a spectrometer and a streak camera. As illustrated in Fig. 1, the measurement was performed at an axial line of sight. An optical collector coupled to an optical fiber was positioned along the axis of symmetry of the vessel, ∼0.4 m from the center. The optical collector functioned primarily to collect parallel light. The light emitted by the plasma near the central axis was focused into the fiber optic by the optical collector and was then transmitted to the diagnostic system. The scan speed of the streak camera was optimally set, resulting in a measurement time resolution of ∼0.05 μs. According to the method presented in Ref. 45, temporal profiles of the electron density and temperature in the second half-cycle can be extracted from the time-dependent H_β spectra. Simultaneously, a visible-light fast framing camera was utilized to obtain time-series images of the pinch plasma evolution. Positioned on one side of the vessel, this camera was capable of capturing four images concurrently. The temporal interval between two consecutive images was set to 1.0 μs, and the exposure duration for a single image was established at 15 ns. All the experimental operations were synchronized through a high-precision control unit where a digital delay generator was applied.

Figure 3(a) shows time-series images of the bulk plasma motion during the second pinch half-cycle. The zero point of the temporal markers in all frames corresponds to the commencement of the second half-cycle, specifically 240.0 μs. Two shots were conducted under the same conditions, each capturing a sequence of four frames. Experimental evidence has demonstrated that our experiment exhibits commendable reproducibility for shot-to-shot discharge.45 Therefore, the outcomes from both shots can be feasibly connected in time and space. Figure 3(a) shows the initial state of the implosion process at 242.0 μs, during which a toroidal plasma forms near the vessel wall. According to the fundamental principles of theta pinch, an azimuthal current sheet exists within the toroidal plasma. This current sheet is driven by an increasingly strong J_θ × B_z force in the magnetic field B_z, which initiates the subsequent implosion spanning from 242.0 to 249.0 μs. Throughout the implosion process, the background plasma between the toroidal plasma and the axis undergoes rapid disturbances. Figure 3(b) shows the radial motion trajectory of the plasma outer boundary extracted from Fig. 3(a), reflecting the state of the background plasma under disturbance. Observations indicate that during the implosion, the background plasma undergoes a detailed sequence of initial compression, followed by expansion, and then recompression. For convenience, the two compression stages are named the first compression and the second compression, respectively.

Figure 4 shows the measured temporal profiles of electron density and temperature, along with the luminosity variation in the extension tube during the corresponding time periods. The density profile reflects the compression–expansion–recompression dynamic process experienced by the plasma, exhibiting a trend of initial increase, followed by a decrease, and then a subsequent increase. The temperature continues to increase over a long observation period until it suddenly drops at 248.8 μs. At this moment, the luminosity in the extension tube begins to rise (see Fig. 4). Clearly, the drop in temperature is caused by the heat conduction resulting from the interaction between the plasma jet and the background medium in the extension tube.

From Fig. 3(b), the initial velocity for the first compression (242.0–245.0 μs) is approximately v₁ = 2.4 × 10⁴ m/s, and the initial velocity of the second compression (247.0–249.0 μs) is about v₂ = 1.3 × 10⁴ m/s. According to Fig. 5, the initial temperature and initial density of the background plasma during the first compression are 2.10 eV and 0.70 × 10¹⁶ cm⁻³, respectively, while the initial temperature and initial density during the second compression are 3.94 eV and 1.05 × 10¹⁶ cm⁻³, respectively. Consequently, the initial acoustic Mach number during the first compression can be calculated as M_S1 = v₁/V_S1 ≈ 1.66, while the initial magnetoacoustic Mach number is M_MS1 = v₁/V_MS1 ≈ 0.94, where V_S, V_A, and VMS=VA2+VS2 are the sound speed, Alfvén speed, and magnetoacoustic speed in the background plasma, respectively. This indicates that the background plasma is influenced by hydrodynamic shocks during the initial phase of the first compression. However, in the experiment, measurements of plasma temperature, density, and magnetic fields are conducted along the axis. Consequently, to effectively study radiation properties during magnetized plasma compression, it is necessary to consider the conditions near the axis, treating the near-axis plasma as the subject of study. As shown in Fig. 3, the compression velocity of the plasma near the axis during the first compression has decreased to ∼1.0 × 10⁴ m/s (i.e., 1 cm/μs), corresponding to an acoustic Mach number of MS1′≈0.58. This suggests that the near-axis plasma undergoes adiabatic compression and heating during the first compression. By contrast, the second compression consistently occurs near the axis, with an initial acoustic Mach number M_S2 = v₂/V_S2 ≈ 0.63 and an initial magnetoacoustic Mach number M_MS2 = v₂/V_MS2 ≈ 0.59; thus, the near-axis plasma in the second compression also experiences adiabatic compression and heating. For convenience, the last microsecond of the first compression and the initial microsecond of the second compression are selected as the subjects of study, marked as Stage-1 and Stage-2 in Fig. 4. Both of these sub-stages occur near the axis, during which the plasma undergoes adiabatic compression and heating. It is important to highlight that the measured magnetic fields used to calculate the Alfvén velocity in the above two cases are derived from Fig. 2 and are 0.08 and 0.04 T, respectively.

It is widely recognized that the J_θ × B_z force exerted on the current sheet plays a pivotal role in driving the dynamic evolution of theta pinch plasmas.48 For the cylindrically shaped theta pinch presented in this work, B_z = B_d + B is the net magnetic field parallel to the cylinder axis, with external driving field B_d and internal trapped field B. The current density J_θ in the current sheet is associated with an azimuthal induced electric field E_θ = η_⊥ · J_θ, where η_⊥ is the transverse Spitzer resistivity. Figure 5(a) illustrates the detailed evolution of the axial magnetic field B during the compression of the magnetized plasma, with a corresponding comparison drawn against magnetic field B₀ measurements taken in the absence of plasma generation (specifically, a 20 kV discharge without working gas). In fact, B₀ can be considered as the driving field B_d in the context of magnetized plasma compression. It can be found that the magnetic field trapped in the plasma is antiparallel to the external driving magnetic field at the start of the half-cycle. This clarifies why plasma compression initiates after ∼242.0 μs: the inward magnetic pressure is lower than the outward one prior to that point. Interestingly, Figs. 4 and 5 together show that the temporal evolution of the magnetic field B is decoupled from that of the density, particularly during Stage-1 of the first compression. According to purely ideal or resistive magnetohydrodynamics (MHD),17,49 the changes in plasma density are coupled with those in the magnetic field, exhibiting a positive correlation. However, our experimental results show characteristics that contradict this conclusion: the magnetic field decreases rapidly (see Fig. 5), in contrast to the gradual rise in the density (see Fig. 4). These suggest the presence of a magnetic transport mechanism beyond purely ideal or resistive MHD, which leads to demagnetization of the central plasma during the magnetized plasma compression.

During the first compression phase, an average temperature of 2.5 eV, an average density of 8.5 × 10¹⁵ cm⁻³, and an average magnetic field B of 0.25 T are determined. This gives a ratio of the cyclotron frequency ω_c and the collision frequency 1/τ_e, i.e., Hall parameter, of ω_cτ_e ≈ 1.3. The magnetic field transport in such plasmas is governed by extended MHD (Ex-MHD):27,29∂B∂t=∇×vB×B+∇×η⊥μ0∇×B+∇Te×∇neene,(1)where the first term describing advection is combination of the hydrodynamic motion and the Nernst advection as v_B ≈ v + v_N under our magnetized condition, for bulk plasma motion v and Nernst advection v_N. During the first compression phase, an average sound speed of 1.6 × 10⁴ m/s and an average thermal diffusivity of 38 m²/s are determined, giving a thermal Péclet number Pe ∼ 21. This makes heat convection dominant over heat conduction, indicating the insignificance of Nernst advection. The second term is resistive diffusion with transverse Spitzer resistivity η_⊥. Our plasma parameters give an average value of η_⊥ ∼ 1.5 × 10⁻⁴ Ω · m. A scale length of 0.05 m, the typical radius of the plasma column, gives a magnetic Reynolds number Re_M ≳ 25, while a distance of ∼0.01 m, the characteristic length scale of bulk plasma motion on a characteristic time scale (10⁻⁶ s), gives Re_M ∼ 5. The large Re_M associated with the system size allows us to neglect magnetic diffusion described by the second term in Eq. (1). However, the modest value of Re_M ∼ 5 suggests that while magnetic field advection is anticipated, magnetic diffusion will become important on the characteristic length scale of bulk plasma motion. The final term corresponds to the generation of magnetic fields resulting from the Biermann battery effect, which is negligible in the cylindrically symmetric geometry because ∇T_e‖∇n_e. Therefore, under our conditions, the primary factors influencing variations in the magnetic field are the predominant hydrodynamic advection and the probable magnetic diffusion on a small length scale.

To further determine the mechanism of magnetic transport during the first compression, we introduce the azimuthal component of the generalized Ohm’s law to describe magnetic transport:26,50Eθ=Eθd+Eθp+Ev×B,(2)where E_θ = η_⊥ · J_θ is the total electric field induced in the current sheet. The first term on the right, E_θd, represents the electric field induced by changes in the driving magnetic field B_d and is directly proportional to the driving current or driving magnetic field.51 According to Fig. 2, the measured driving current increases monotonically throughout the entire duration of the implosion, and consequently E_θd is also monotonically increasing. The second term, E_θp, represents the electric field induced by changes in the magnetic field due to plasma currents, which is negligible in our situation.50 The bulk plasma motion across the field lines generates the third term, E_v×B, called the motional electric field. Through the application of Stokes’s theorem and Faraday’s law,∮LEθ⋅dl=∯S∇×B⋅ds,(3)∇×Eθ=−∂B∂t,(4)the relationship between E_θ and the internal field B surrounded by the current sheet can be deduced:∮LEθ⋅dl=∯S−∂B∂t⋅ds.(5)Assuming a spatially uniform magnetic field B, the integration of Eq. (3) at a radius R of the current sheet yieldsEθ=R2−∂B∂t.(6)On the characteristic time scale of 10⁻⁶ s in our work, the impact on E_θ of variations in R caused by the bulk plasma motion is negligible, and soEθ∝−∂B∂t.(7)Consequently, the mechanism of magnetic transport can be understood by combining Eqs. (2) and (7) with the derivative of the measured magnetic field B.

The measurement of ∂B/∂t is shown in Fig. 5(a). Combining these with the generalized Ohm’s law (2), illustrations of magnetic transport are presented in Fig. 5(b). The labels (i)–(iv) in Fig. 5(a) represent four evolutionary phases of E_θ, corresponding to the four illustrations in Figs. 5(b-i)–5(b-iv), respectively. Figure 5(b-i) illustrates the magnetic field configurations and induced electric fields at the onset of the first compression. In phase (i), the counterclockwise-flowing driving current I_d generates a magnetic field B_d perpendicular to the page and pointing outward. The rapidly increasing B_d induces a continually increasing electric field E_θd within the current sheet in the clockwise direction. The J_θ × B_z force acting on the current sheet drives the bulk plasma motion across magnetic field lines, generating a motional electric field E_v×B. As the magnetic field surrounded by the current sheet is perpendicular to the page and pointing inward, E_v×B has the same direction as E_θd. Consequently, the total induced electric field E_θ within the current sheet increases continually with increasing E_v×B and E_θd in the clockwise direction.

In phase (ii), however, E_θ decreases rapidly to zero [see Fig. 5(a-ii)]. The discussion above has demonstrated that the term E_θd is monotonically increasing throughout the whole range of investigation. Therefore, the only possible factor causing the decrease in E_θ is the change in E_v×B. The observation of bulk plasma motion in Fig. 3 suggests that the plasma remains compressed radially inward in this phase. If all the magnetic flux trapped in the plasma remains perpendicular to the page and directed inward, then the term E_v×B will continue to enhance E_θ in the clockwise direction. Hence, the fact of decreased E_θ implies that the reversed field B_d likely diffuses into the plasma. This can be confirmed through a simple evaluation as follows. We have demonstrated that magnetic diffusion will become important on the characteristic length scale (0.01 m) of bulk plasma motion, where a modest magnetic Reynolds number of Re_M ∼ 5 is estimated. In phase (ii), the plasma bulk velocity is estimated from Fig. 3(b) to be v_ii ≈ 1.2 × 10⁴ m/s, and so a length l_ii ∼ 0.012 m of the plasma across field lines is obtained on the characteristic time scale of τ ∼ 1.0 × 10⁻⁶ s. As a comparison, the magnetic diffusion time is evaluated as t_diff ∼ 1.2 × 10⁻⁶ s, considering the length l_ii and the plasma resistivity of η_⊥ ∼ 1.5 × 10⁻⁴ Ω · m. Consequently, we can obtain the relation t_diff ∼ τ, which indicates that magnetic diffusion can couple well with the bulk plasma motion. This highlights the importance of magnetic diffusion at the plasma boundary. The inward compression of the plasma necessitates the external driving field B_d to be greater than the internal field. The resulting gradient in magnetic field will naturally induce diffusion of B_d into the plasma, as illustrated in Fig. 5(b-ii). With this magnetic field configuration, bulk plasma motion will induce two components of E_v×B, which have opposite directions in azimuth: the original internal field generates a clockwise electric field component, while the driving field diffused into the plasma produces a counterclockwise electric field component. When the component associated with diffusion magnetic field is sufficiently significant, the counterclockwise net E_v×B will counterbalance and even exceed the increase in the clockwise term E_θd, resulting in a decrease in the total induced electric field E_θ. As more driving magnetic fields diffuse into the plasma, an extreme scenario is anticipated: the counterclockwise component of E_v×B will surpass the sum of its clockwise component and the E_θd term, leading to an increase of E_θ in the counterclockwise direction. Figure 5(a) shows that this scenario occurs during phase (iii). When a counterclockwise E_θ is induced and progressively intensified, the internal magnetic field pointing outward from the page will experience rapid attenuation following Faraday’s law. Concurrently, the J_θ × B_z force acting on the current sheet changes to radially outward, exerting a decelerating effect on the plasma compression. This explains why demagnetization of the plasma center and deceleration of plasma compression are observed in phase (iii).

Figure 5(b-iv) shows the dynamics and electromagnetic field configuration of the plasma during phase (iv), which occurs after the end of the first compression. At this point, the plasma expands radially outward under the combined effects of hydrodynamic pressure and the J_θ × B_z force. As the plasma expands, the clockwise component of E_v×B increases, while the counterclockwise component decreases. Although this reduces the counterclockwise E_θ, before E_θ reverses direction, it will collaborate with the inward-diffusing magnetic field B_d to facilitate demagnetization of the central plasma until the original magnetic field is cavitated.

The above results and discussion demonstrate a possible mechanism for the demagnetization of magnetized plasma: in a compressed state under an opposing external magnetic field, the magnetized plasma induces an electric field that weakens the existing internal magnetic field owing to the diffusion of the external field into its interior. The essence of this demagnetization mechanism lies in the coupling effect between magnetic diffusion and hydrodynamic advection at the plasma boundary, which also causes a deceleration effect on the plasma compression. From the experimental results, one can also derive a criterion for assessing the significance of this magnetic transport mechanism. For plasma moving at a bulk velocity v perpendicular to the magnetic fields, the length scale across the magnetic fields within its characteristic evolution time scale τ is L = vτ. Assuming the transverse Spitzer resistivity of the plasma to be η_⊥, the magnetic diffusion time for this length scale L is t_diff = μ₀L²/η_⊥. The magnetic transport mechanism mentioned above requires that the resistive diffusion term be comparable to, or even surpass, the hydrodynamic advection term, with the condition t_diff ≲ τ, and gives the criterionη⊥≳μ0v2τ.(8)Therefore, for a magnetized plasma compression system with known resistivity and characteristic time scale, meeting criterion (8) becomes easier as the plasma bulk velocity decreases. Using a simple estimation to test criterion (8), it is evident that the plasma conditions (v_i ∼ 2.4 × 10⁴ m/s, τ ∼ 10⁻⁶ s) in phase (i) as shown in Fig. 5 do not satisfy the criterion, leading to the main observation of a rapid increase in the magnetic field.

The demagnetization and deceleration behavior reported here can be generalized to the many other situations in which a magnetized plasma is compressed by a reverse driving magnetic field. We try to expand the applicability of criterion (8) in the contexts of inertial confinement fusion (ICF) and astrophysics.

A possible example is the magnetized ICF experiments, where a compressed central core magnetic field over 10³ T is applied to improve implosion performance.19 The magnetic fields self-generated in relevant ICF experiments by the Biermann effect are anticipated to exceed 10⁴ T,25,33 and are believed to wrap around the hot-spot edge owing to Nernst advection.43 If the Biermann field at the edge has a strong component antiparallel to the applied field at the hot-spot core, similar demagnetization and deceleration phenomena may be present during the implosion. Both effects could reduce the effectiveness of magnetized fusion techniques. Using criterion (8), a simple assessment is as follows. The Biermann effect has been demonstrated to generate 90% of magnetic flux in the final 1 ns of the ICF implosion.43 This time frame typically encompasses the stagnation phase,33 during which the implosion kinetic energy is converted into internal energy as the implosion velocity decreases. During the stagnation phase, the inward compression velocity of the fuel plasma can be approximated as v ≲ 10⁴ m/s, primarily because of the lower implosion velocity of around 100 km/s in magnetized ICF systems.17 Considering a typically characteristic time scale τ ∼ 10⁻¹¹ s,34 the right-hand term of criterion (8) can be estimated as μ₀v²τ ≲ 10⁻⁹ Ω · m. According to Refs. 25 and 34 regarding the Biermann field, the typical plasma parameters at the edge of the ICF hot spot (n ∼ 10³² m⁻³, T ∼ 10³ eV) yield a Spitzer transverse resistivity η_⊥ ∼ 10⁻⁸ Ω m. These assessments indicate that criterion (8) is fully satisfied during the stagnation phase in magnetized ICF systems. Therefore, it is highly likely that relevant demagnetization and deceleration effects may occur in magnetized ICF experiments. These findings hold significant value for an ongoing series of such experiments being conducted on the OMEGA cylindrical implosion platform.17,52,53

Another highly relevant example involves the behavior of planetary magnetospheres under extreme solar wind conditions. In this scenario, magnetosphere plasmas sandwiched between the magnetopause and the planetary surface experience compression due to the dynamic pressure of the solar wind. When the solar wind impacts the magnetosphere at a large magnetic shear angle across the magnetopause (∼180°), a magnetized plasma compression system suitable for criterion (8) is formed. We note that observations of Mercury’s magnetosphere by the MESSENGER spacecraft reported a reduced altitude of the subsolar magnetopause during extreme solar wind intervals much lower than model predictions.21 The models include a shielding effect provided by induction currents in Mercury’s interior, which add to the closed magnetic flux in the dayside magnetosphere and temporarily increase Mercury’s magnetic moment.54 The investigations reported in Ref. 21 suggest that the difference between the observations and the models is most likely the result of strong dayside reconnection driving magnetic flux erosion and thus negating the induction effect. Given that the physical system of Mercury’s magnetosphere compression by the solar wind easily meets the conditions of the case in this study, the demagnetization mechanism governed by criterion (8) provides a possible contribution to the reduction in altitude of the subsolar magnetopause. If this demagnetization mechanism is active during the solar wind interaction with Mercury’s magnetosphere, then the shielding provided by the induction effect will be weakened. Consequently, in this scenario, the magnetic reconnection rate obtained in Ref. 21 is likely to be an overestimate.

The preceding results demonstrate a strong coupling between magnetic transport and the hydrodynamic behavior of the magnetized plasma. In general, the changes in hydrodynamics transform into significant variations in the core temperature and density throughout the magnetized plasma compression.17 The radiation emission from the plasma exhibits a high sensitivity to these variations. Consequently, it is anticipated that a correlation can be established between the magnetic transport and radiation properties during magnetized plasma compression.

In our experiments, the radially inward J_θ × B_z force acting on the current sheet drives the plasma implosion. It is clear from the preceding discussion that the plasma experiences two stages of radial compression before undergoing axial ejection. A comparative analysis of the characteristics of the two compression stages facilitates understanding of the relationship between magnetic field transport and radiation properties. Here, we focus on the last 1 μs of the first compression stage (labeled as Stage-1) and the initial last 1 μs of the second compression (labeled as Stage-2). As mentioned earlier, during these two small stages, the plasma undergoes adiabatic compression near the central axis. In the case of adiabatic compression, the evolution of the plasma parameters before and after the compression is governed by the adiabatic relation55Tf/Ti=(nf/ni)2/3, which is plotted in Fig. 6. For comparison, the experimental data pertaining to T_f/T_i vs n_f/n_i for the two compression stages is also presented, utilizing the temperature and density measurements from Fig. 4. In Fig. 6, the experimental data for the two stages show notable deviations from the adiabatic compression curve.

The above discussion indicates that there are deviations between the experimental results and the theoretical curve for both Stage-1 and Stage-2. From the comparison in Fig. 6, it is easy to see that the primary factor contributing to these discrepancies is the energy loss experienced by the plasma throughout the compression process, leading to a reduction in the “final state” temperature T_f of the plasma. In general, the possible energy loss mechanisms of a plasma include heat conduction and radiation emission. In our case, the conduction loss should be very weak or even negligible, because the plasma is almost isolated from the walls and ambient medium. This indicates that radiation loss serves as the predominant mechanism for the plasma losing energy during Stage-1 and Stage-2.

Possible radiative loss mechanisms include continuum radiation and line-emission radiation. Continuum radiation typically arises from recombination radiation (RR), bremsstrahlung (Br), and cyclotron radiation (CR). The powers of these mechanisms for a hydrogen plasma can be estimated as follows:44PRR=1.3×10−32n2T−1/2W/cm3,(9)PBr=5.0×10−31n2T1/2W/cm3,(10)PCR=6.21×10−25B2nTW/cm3,(11)where n and T are the plasma electron density in cm⁻³ and temperature in keV, respectively. B is the magnetic field in gauss. Based on our plasma parameters, a simple estimation gives P_RR ∼ 10P_Br ∼ 10⁵P_CR. Therefore, recombination radiation is the main channel producing the continuum radiation. We can estimate the average recombination radiation powers of Stage-1 and Stage-2, where P_RR-1 ≈ 21 W/cm³ and P_RR-2 ≈ 30 W/cm³, respectively. However, these power losses are inadequate to explain the deviations between the experimental results and the theoretical curve in Fig. 6, which will now be discussed. The increase in power density as a result of the plasma compression is56ΔP=kB⋅Δn⋅ΔT/ΔtW/cm3,(12)where k_B is Boltzmann’s constant, Δn and ΔT are the increments in electron density and temperature, respectively, during the plasma compression, and Δt is the duration of the compression. According to Δn and ΔT from the adiabatic compression curve (Fig. 6), the theoretical (without energy loss) increases of power density in Stage-1 and Stage-2 are 6.3 × 10² and 4.4 × 10² W/cm³, respectively. By contrast, the experimental power density increments show smaller values of 2.3 × 10² W/cm³ for Stage-1 and 1.7 × 10² W/cm³ for Stage-2. These results imply energy loss powers of P_loss-1 ≈ 4.0 × 10² W/cm³ and P_loss-2 ≈ 2.7 × 10² W/cm³ in Stage-1 and Stage-2, respectively. Given that P_loss-1 ≫ P_RR-1 and P_loss-2 ≫ P_RR-2, it is essential to take into account additional loss mechanisms beyond continuum radiation, specifically line-emission radiation.

Within a hydrogen plasma system, the line emissions consist predominantly of visible Balmer line series and deep ultraviolet Lyman line series. For an energy level transition n to m in a hydrogen atom, the power of line radiation is given by44Pline=5.1×10−25fnmgmnn1g1T1/2ΔEnmΔEn13e−ΔEn1/TW/cm3,(13)where f_nm is the oscillator strength, g_m is the statistical weight of level m, ΔE_nm = E_n − E_m is the energy level difference, n and T are the plasma electron density and temperature, respectively, and n₁ ≈ 0.04n is the ground-state atom density inferred in Ref. 56 under comparable experimental conditions. To provide a rough estimate of the line-radiation power, we choose the strongest emissive alpha line (n = 3, m = 2) in the Balmer series for comparison. As per Eq. (13), the powers of the Balmer alpha line are P_alpha-1 ≈ 1.7 × 10² W/cm³ for Stage-1 and P_alpha-2 ≈ 7.6 × 10² W/cm³ for Stage-2. These results indicate that the power densities of the line radiation P_line are comparable in magnitude (∼10² W/cm³) to those of the energy loss P_loss, for both Stage-1 and Stage-2. Therefore, the line radiation loss is likely the dominant energy loss mechanism responsible for the observed deviations in Fig. 6.

Line emission is known to occur in an atom system where electrons in the excited state transition from higher energy levels to lower energy levels, emitting photons in the process. However, the diagnostic results presented in Fig. 4 reveal complete plasma ionization across the study range. This suggest that line emission derives predominantly from neutral atoms generated through ion–free-electron recombination mechanisms. Similar experimental conditions have demonstrated the significance of these mechanisms, with confirmation of the existence of two possible recombination pathways.56 The first is radiative recombination (RR) and the second is three-body recombination (TR). The corresponding recombination rates can be estimated as follows:57νRR=2.7×10−13T−3/4ncm3/s,(14)νTR=5.6×10−27T−9/2n2cm3/s,(15)where T and n are the electron temperature and density of the plasma. Utilizing the T and n data shown in Fig. 4, the profiles of ν_RR and ν_TR are presented in Fig. 7. Luminosity_jet shown in Fig. 4 indicates that there is almost no luminosity in the extension tube before 249 μs. Therefore, Luminosity_total shown in Fig. 7 can be attributed primarily to the self-luminosity of the main plasma within the vessel. It is evident that the evolutionary trends of the two recombination rates ν_RR and ν_TR are consistent with the behavior of the luminosity. In particular, the luminosity rises as the recombination rates increase in both Stage-1 and Stage-2. These findings further confirm that energy loss in Stage-1 and Stage-2 is dominated by the line radiation mechanism, since the line emission originates mainly from neutral atoms generated via three-body recombination and radiative recombination in the plasma.

Furthermore, an intriguing finding from Fig. 7 is that the values of the luminosity and recombination rates are greater in Stage-1 than in Stage-2, suggesting a greater radiation loss in Stage-1 than in Stage-2. This is consistent with the result in Fig. 6 wherein the deviation between experimental data and theoretical curve in Stage-1 is larger than that in Stage-2. The differences in radiation loss between these two stages can be explained by considering the variations in magnetic transport mechanisms present within them. We find a close correspondence between Stage-1 in Figs. 4 and 7 and phase (iii) in Fig. 5. During Stage-1, the plasma experiences a demagnetization process as it is compressed, resulting in a reduction of the axial magnetic field from 0.41 to 0.24 T. By contrast, the magnetic field exhibits a rapid increase from 0.04 to 0.26 T in Stage-2. In a magnetized plasma compression system, the total input energy is converted into thermal and magnetic energy, thereby boosting both thermal pressure (∼2nk_BT) and magnetic pressure (∼B²/2μ₀). Changes in magnetic pressure directly influence the thermal pressure owing to energy conservation. This influence is emphasized when the ratio of thermal pressure to magnetic pressure no longer satisfies the condition β ≫ 1.52 Regarding Stage-1 and Stage-2 in our study, the plasma conditions (with a density n ∼ 10¹⁶ cm⁻³, temperature T < 5 eV, and magnetic field B ∼ 2 T) yield a ratio β ∼ 1. This suggests that thermal pressure exhibits high sensitivity to changes in magnetic pressure. In Stage-1, a 41% reduction in the plasma magnetic field decreases the magnetic pressure, thereby improving the compressibility of the plasma. As a result, the plasma density increases, manifested as a rise in thermal pressure. This increase in density is more pronounced compared with the scenario in which magnetic pressure changes are not considered, leading to further density enhancement. From Eq. (13), an increased density is beneficial to enhancing the power density of line radiation. Furthermore, Eqs. (14) and (15) suggest that the density evolution affects the rates of the radiative recombination and three-body recombination processes. The additional increase in density contributes to the generation of more of the neutral atoms necessary for line emission, thereby increasing the line radiation loss in the system. By contrast, in Stage-2, an increase in the magnetic field by a factor of 6.5 boosts the magnetic pressure, thereby reducing the compressibility of the plasma and inhibiting the increase in density. As a result, there are decreases in the power density for line radiation and the recombination rate essential for producing neutral atoms, compared with the case where magnetic pressure changes are neglected. Consequently, Stage-1 exhibits a greater radiation loss than Stage-2.

The above results demonstrate a significant influence of magnetic field variations on the radiative properties of magnetized plasmas with β ∼ 1. This influence is manifested as magnetic field variations changing the compressibility of the plasma, and subsequently altering the evolution of plasma density closely associated with its radiative properties. In other words, magnetic transport processes affect the radiative properties of a magnetized plasma by influencing its hydrodynamic behavior. In our case, the dominant mechanism by which the compressed plasma loses energy is line-emission radiation. The magnetic transport changes the plasma density and then the power density of radiation loss. This effect will be of great interest to the magnetized ICF community. For instance, the dominant radiative loss in the magnetized ICF scenario is due to bremsstrahlung radiation, the power density of which is known to be directly proportional to the square of the plasma density n, i.e., P_Br ∝ n². Studies of magnetized ICF conducted on a cylindrical implosion platform at OMEGA have revealed that in a magnetized hot spot with β ∼ 1, the core density experiences a significant reduction due to the compression of the magnetic field.17,52 Therefore, we infer a notable suppression in radiation loss from the hot spot when the magnetic pressure is non-negligible compared with the thermal pressure, which may help improve the effectiveness of magnetized fusion techniques. However, the magnetic pressure increases in the hot spot at the expense of the thermal pressure (mainly suppressing the increase in density),52 which is unfavorable for ignition according to the Lawson criterion.58 Thus, determining an optimal magnetic field conducive to fusion yield requires a comprehensive consideration of these effects.

The finding that magnetic transport processes influence the radiative properties of a magnetized plasma could be particularly relevant to tokamak fusion systems18 and certain astrophysical phenomena such as magnetized bow shocks and heterogeneous outflows.7,15 Radiative cooling has been demonstrated to play a crucial role in the collimation of astrophysical outflows and in the formation and evolution of bow shocks.7,59 In these situations, the magnetic pressure in plasmas is non-negligible compared with the thermal pressure, and some plasmas even exhibit β ≲ 1.

This study has investigated the magnetic transport mechanisms and radiation properties in a magnetized plasma undergoing compression. We have observed an anomalous demagnetization phenomenon during the compression process of the magnetized plasma, wherein the magnetic field at the center of the plasma becomes weaker with increasing density. The occurrence of this demagnetization phenomenon depends on the presence of an external magnetic field that is antiparallel to the internal field on the outer side of the compressed plasma. Our analysis, based on a combination of Ex-MHD theory and a generalized Ohm’s law, has revealed this demagnetization mechanism: the external magnetic field diffuses through the plasma boundary and couples with hydrodynamic advection, generating an electric field that depletes the central magnetic field. Additionally, the interaction between this electric field and boundary magnetic fields can decelerate the plasma compression. Significantly, we have proposed a straightforward criterion to assess the effectiveness of this demagnetization mechanism during the magnetized plasma compression. Particularly in the context of magnetized ICF, we have utilized this criterion to demonstrate the potentially substantial impact of the reported demagnetization mechanism, especially in cylindrical implosion experiments.17,52,53 Furthermore, this demagnetization mechanism may also affect the interactions between the solar wind carrying southward interplanetary magnetic fields and the magnetospheres, resulting in a lower magnetopause standoff altitude.

In addition, experimental results have revealed a strong correlation between magnetic transport and radiation properties, particularly evident for magnetized plasmas with β ≲ 1. The variation in the magnetic field changes the compressibility of the plasma during the compression, thereby altering the density evolution associated with radiation properties and consequently affecting the radiation loss of the plasma. Essentially, the hydrodynamical behavior of the magnetized plasmas plays a bridging role in correlating magnetic transport and radiation properties. This mechanism warrants significant attention in optimizing magnetized ICF implosion design, since the power of bremsstrahlung, which dominates energy loss, is highly sensitive to plasma density changes. Moreover, in other scenarios such as tokamak plasmas,18 astrophysical plasma outflows,7 and bow shocks,15,59 the magnetic pressure is crucial and cannot be overlooked relative to thermal pressure. Therefore, the mechanism reported here holds great significance in understanding the behavior of plasmas in these situations as well.

Acknowledgment. The authors are grateful for the support of the State Key Development Program for Basic Research of China (Grant No. 2022YFA1602503) and the National Natural Science Foundation of China (Grant Nos. 12120101005 and 12205247). The authors thank Professor Bingli Zhu for his technical support with the streak camera (T10) and framing camera (Zolix Instruments Model FC-4-S-VIS of the T-lab series). We are also grateful to Dr. Liangwen Qi for technical support and discussions of magnetic field measurements.