The Sun, being an active star, undergoes eruptions of magnetized plasma that reach the Earth and cause the aurorae near the poles. These eruptions, called coronal mass ejections (CMEs), send plasma and magnetic fields out into space. CMEs that reach planetary orbits are called interplanetary coronal mass ejections (ICMEs) and are a source of geomagnetic storms, which can cause major damage to our modern electrical systems with limited warning. To study ICME propagation, we devised a scaled experiment using the Big Red Ball (BRB) plasma containment device at the Wisconsin Plasma Physics Laboratory. These experiments inject a compact torus of plasma as an ICME through an ambient plasma inside the BRB, which acts as the interplanetary medium. Magnetic and temperature probes provide three-dimensional magnetic field information in time and space, as well as temperature and density as a function of time. Using this information, we can identify features in the compact torus that are consistent with those in real ICMEs. We also identify the shock, sheath, and ejecta similar to the structure of an ICME event. This experiment acts as a first step to providing information that can inform predictive models, which can give us time to shield our satellites and large electrical systems in the event that a powerful ICME were to strike.

Coronal mass ejections (CMEs) are solar eruptions that result in bubbles or loops of plasma from the solar corona and often interact with surrounding solar wind plasma and magnetic fields.1 These eruptions can propagate through the solar system into planetary orbits and are called interplanetary CMEs or ICMEs. Figure 1(a) shows a diagram of an ICME. In the figure, the looped structure represents the flux rope propagating away from the Sun (yellow dot) toward the Earth (blue dot) while pushing a shock (curved line) ahead of it. CMEs start off as bubbles of plasma contained by the Sun's magnetic field stretching out into its corona. CMEs are the violent result of magnetic reconnection on the Sun, and their formation is the subject of many research projects.2,3 CMEs are often highly magnetized and have an embedded magnetic field structure, called a flux rope, inside it. The frequency of CME formation generally follows the 11-year solar cycle of sunspots, with more CMEs forming closer to solar maximum and less forming closer to solar minimum.4 

FIG. 1.

(a) Schematic of an ICME traveling through the IM adapted from Young and Kuranz.8 The curved structure is the ejecta with the looping flux rope magnetic field propagating from the Sun (yellow dot) toward the Earth (blue dot). (b) Setup inside the BRB. CTI (compact torus injector) launches the scaled ICME. The CT (compact torus) is the plasma ejecta of the scaled ICME. B H is the background magnetic field provided by the Helmholtz coils. The colored lines represent the diagnostics used in the experiment and their approximate positions on the BRB.

FIG. 1.

(a) Schematic of an ICME traveling through the IM adapted from Young and Kuranz.8 The curved structure is the ejecta with the looping flux rope magnetic field propagating from the Sun (yellow dot) toward the Earth (blue dot). (b) Setup inside the BRB. CTI (compact torus injector) launches the scaled ICME. The CT (compact torus) is the plasma ejecta of the scaled ICME. B H is the background magnetic field provided by the Helmholtz coils. The colored lines represent the diagnostics used in the experiment and their approximate positions on the BRB.

Close modal

Once the ejecta, the plasma of the CME, detaches from the Sun, it is sent through the solar system at speeds that may exceed the interplanetary medium's (IM's) magnetosonic speed, c ms , which is the speed at which a wave driven by thermal and magnetic pressures can travel. This creates a shock in front of the ejecta. Behind the shock, but in front of the ejecta, the plasma from the IM builds up and creates a sheath region that varies intensely in temperature, density, and magnetic field. During this time, the ejecta expands adiabatically and decreases its temperature. Once a CME reaches planetary orbits, it becomes an interplanetary CME or ICME. ICMEs that contain large and smoothly rotating magnetic fields from its flux rope structure, in addition to a lower proton temperature, are called magnetic clouds, which are a specific subset of ICMEs, making up about 30% of the total.5 The scaled ICMEs generated in this experiment do not fully retain their flux rope magnetic structure and, therefore, are less related to magnetic clouds. The work of this paper is more relevant to nonmagnetic cloud ICMEs and will refer to them simply as ICMEs.

ICMEs are large dynamic structures that can contain 1012 kg of solar plasma, travel at speeds between 250 and 3000 km/s, and take anywhere between 18 h and several days to reach the Earth. By the time an ICME arrives, it has a length scale of about 3.0 × 10 7  km or 0.25 AU, where 1 AU (astronomical unit) is the distance from the Earth to the Sun ( 1.5 × 10 8  km).6 The interactions between the Earth's geomagnetic field and an ICME result in geomagnetic storms and other severe space weather.7 ICMEs are able to increase the strength of polar aurorae, disable satellites, and damage terrestrial electronics, depending on their size and structure.

When an ICME interacts with the Earth's magnetic field, the shock and the sheath cause geomagnetic storms that can affect terrestrial electrical systems. For example, the Carrington Event in 1859 is the most severe geomagnetic storm recorded, and it caused aurorae in lower latitudes as well as sparking and even fires in several telegraph systems.9 Also, in March 1989, multiple ICMEs contributed to a geomagnetic storm that damaged transformers of power systems throughout Canada, the USA, and Europe.10 The Sun is still active and events of similar magnitude, if they were to strike the Earth today, would create more problems as more people depend on things like internet, GPS, and other electrical systems that would be damaged or destroyed by the ICME.

There are plenty of ICME events powerful enough to do similar or greater damage but, luckily, they miss the Earth. For example, Baker et al. analyzed an ICME from July 2012 that nearly missed the Earth and would have caused a magnetic disturbance similar to or worse than the Carrington Event.11 Studying the formation and evolution of ICMEs can help us form better predictive models for ICME behavior. There are a plethora of space weather forecast models that are used to predict the arrival times of ICMEs, but they rely on the limited data received from satellite observations. This, in turn, means that the data gathered are limited to the activity of the Sun, which goes through an 11-year activity cycle.

Measurements of ICMEs are made with satellites usually located at various Lagrange points. Lagrange points are positions in space where the gravitational forces of the Sun and the Earth are balanced with the centripetal force on an object, keeping it in place. These locations are ideal for satellites as they greatly reduce the amount of fuel required to make corrections to the orbit. Satellites such as the NASA Advanced Composition Explorer (ACE) and the Wind spacecraft are placed at Lagrange point 1, which is located 1.5 × 106 km from the Earth and 0.98 AU from the Sun. These spacecrafts use many sensors to measure solar wind properties, such as density, temperature, and magnetic field.

For example, the Wind Magnetic Field Instrument (MFI) consists of two triaxial flux-gate magnetometers, which are magnetic field sensors that can detect fields with magnitudes from 4 nT to well over 65 000 nT with digital resolution as low as ±0.001 nT.12 

Figure 2 shows an example of data collected when an ICME passes over the Wind satellite and displays the shock, sheath, and ejecta regions in the magnetic field, velocity, and total pressure measurements.13 The shock exists at the vertical dashed line labeled a and causes a sudden increase in ion velocity, magnetic field strength, and total pressure. One can identify the sheath, located in the region between the vertical dashed lines a and b, by its highly variable pressure and magnetic fields. The magnetic obstacle, in other words, the ejecta, resides in the region between lines b and c and has a smoother magnetic field. One can infer a rotating flux rope structure from the magnetic components rising and falling at different intervals inside the ejecta.

FIG. 2.

Wind data from an ICME.13 This plot shows normalized magnetic field components ( B x / B ) and magnitude ( | B | ), proton velocity (Vp), and total pressure perpendicular to the magnetic field (Pt), i.e., the sum of magnetic and perpendicular plasma thermal pressures. The x axis is time in hours starting from 10 a.m. of March 19, 2001, to 2 a.m. of March 22, 2001. The vertical line labeled a marks the shock, the section between lines a and b shows the sheath region, and the region between lines b and c is the magnetic obstacle, or the ejecta, of the ICME event.

FIG. 2.

Wind data from an ICME.13 This plot shows normalized magnetic field components ( B x / B ) and magnitude ( | B | ), proton velocity (Vp), and total pressure perpendicular to the magnetic field (Pt), i.e., the sum of magnetic and perpendicular plasma thermal pressures. The x axis is time in hours starting from 10 a.m. of March 19, 2001, to 2 a.m. of March 22, 2001. The vertical line labeled a marks the shock, the section between lines a and b shows the sheath region, and the region between lines b and c is the magnetic obstacle, or the ejecta, of the ICME event.

Close modal

Due to their large length scale, L 3.0 × 10 7  km and low ion density, n i (2.2–17.6)  × 10 3 cm 3 , ICMEs are in the collisionless regime.14 The collisionality of a system can be quantified by the ratio λ i / L , where L is the system size and λi is the ion mean free path, the average distance an ion travels before a collision. For example, the undisturbed IM has an ion density <50 cm−3 and temperature 10 5  K near 1 AU.15 This leads to λ i 10 10  m, which is comparable to the length scale of an entire ICME, and much greater than the size of the shock alone and, therefore, is in the collisionless regime. Schaeffer et al. and Park et al. have created collisionless shocks in the lab using laser-driven plasmas in the high-energy density regime with densities in the range of n 10 19  cm 3 .16,17 The experiment described in this paper also generates collisionless shocks, i.e., λ i / L is small, but with lower densities, n 10 12  cm 3 , along with a larger system size and time scales that allow us to directly probe the plasma with our diagnostics. Also, the astrophysical scaling employed in this paper is important to capture the macrophysics of an ICME/IM system, such as the overall structure of an ICME. With this scaling, we argue that the system provided in the experiment is relevant to an ICME/IM system such that we can identify similar major features in both systems.

This paper is organized as follows: Sec. II discusses scaling requirements and parameters for an astrophysically relevant system, and Sec. III describes our experimental setup. Following the setup, the experimental results are given in Sec. IV. In Sec. V, we discuss how the results are evidence that we have created a scaled experiment and what that means for the future of laboratory research on solar phenomena.

To create a scaled experiment in the laboratory, we must create a laboratory plasma with similar dimensionless parameters as the ICME analog. Young and Kuranz provide a more detailed scaling argument.8 Here, we consider the magnetosonic Mach number, plasma β, and key pressure ratios in the system. Table II displays a comparison of a typical ICME event's dimensionless numbers to that from our experiment.

The magnetosonic speed of a plasma is the speed at which any magnetosonic wave, a wave driven by thermal and magnetic pressures, can travel in the plasma. Therefore, the magnetosonic Mach number attributed to any object propagating through a plasma is M ms = v c ms , where v is the object's speed and c ms is the magnetosonic speed defined as c ms = c s 2 + v A 2 , where cs is the sound speed and vA is the Alfvén speed. The sound speed is defined as c s = γ k T e / m i , where γ is the adiabatic index, k is the Boltzmann constant, Te is the electron temperature, and mi is the mass of an ion. The Alfvén speed is v A = B μ 0 n i m i , where B is the magnetic field, μ0 is the permeability of free space, and ni is the ion number density. To recreate the shock in front of an ICME, we require M ms > 1 . To do that, we adjust the c ms background plasma such that it is below the speed of the scaled ICME ejecta, called a compact torus (CT), which is ∼100 km/s.

Plasma β is the ratio of thermal pressure to magnetic pressure in a plasma, given as β = P th P mag = n i k T B 2 / 2 μ 0 = 2 μ 0 n i k T B 2 . The interplanetary medium near 1 AU has a plasma β of around 1.18 To scale this, we require 1 / 5 < β < 5 for the background plasma as to not become too thermally or magnetically dominated.

The total pressure ratio is P ratio = P tot , in P tot , out , total pressure being the sum of the magnetic and thermal pressures is P tot = P th + P mag . P tot , in is the total pressure inside the ICME ejecta, and P tot , out is the total pressure of the undisturbed IM.

Since ICMEs are diverse phenomena, many different pressure ratios can be justified as well as scaled; here, we require P ratio 2 as a “middle of the road” constraint that is not too large or too small for the Big Red Ball (BRB) to accommodate. A ratio of much lower than 2 is limited by the plasma source used to generate a higher background plasma. The CT is expected to have a relatively high internal pressure, so keeping the background pressure low provides appropriate conditions for this experiment. The total pressure ratio for our experiment will have P tot , in be the total pressure within the CT and P tot , out be the total pressure outside the CT, the background plasma.

These experiments use the Big Red Ball (BRB), pictured in Fig. 3, at the Wisconsin Plasma Physics Laboratory (WiPPL) in Madison, Wisconsin, to create the analog ICME system. The BRB is a 3-m-diameter sphere with samarium cobalt permanent magnets lining the inner surface to confine the plasma inside. Helmholtz coils mounted outside the BRB provide a background axial magnetic field for the ambient plasma that can range anywhere between 0 and 200 Gauss at the center of the BRB. There are over 200 ports on the surface of the vacuum chamber that can be used for diagnostic purpose or as viewing windows into the vessel. Latitude and longitude are used to denote the position of these ports on the vessel, defining the equator as the vertical partition equidistant from the two Helmholtz coils and (0°, 0°) being the topmost position on the BRB.

FIG. 3.

(a) Interior of BRB lined with samarium cobalt permanent magnets. The straight lines are diagnostic probes from the previous experiment. (b) Exterior of BRB showing the upper half of the device. The gray rings are Helmholtz coils that provide the background magnetic field. (c) Diagram of the function of a CTI. Reproduced with permission from Endrizzi, Ph.D. thesis (2021). Copyright 2021 ProQuest.

FIG. 3.

(a) Interior of BRB lined with samarium cobalt permanent magnets. The straight lines are diagnostic probes from the previous experiment. (b) Exterior of BRB showing the upper half of the device. The gray rings are Helmholtz coils that provide the background magnetic field. (c) Diagram of the function of a CTI. Reproduced with permission from Endrizzi, Ph.D. thesis (2021). Copyright 2021 ProQuest.

Close modal

While the ports on the surface of the BRB use spherical coordinates, for measurements inside the BRB, we use cylindrical coordinates. We orient this coordinate system such that the z ̂ direction points along the axis of the Helmholtz coils and r ̂ points radially outward from this axis. This makes for more easily understandable data from the diagnostics we use. Figure 1(b) shows a cartoon of the experimental setup with diagnostics in their approximate positions.

In this experiment, we make an analog to both the interplanetary medium and an ICME. Our goal is to create features consistent with an ICME such as a shock and a sheath region in front of the “ejecta” we inject into the BRB. Our scaled interplanetary medium is the background plasma supplied to the BRB via an array of plasma emitters at its north pole. These emitters, also known as plasma guns, use miniature plasma sources as electron emitters to provide a strong current and voltage to ionize the hydrogen gas pumped into it.20 The Helmholtz coils on the BRB provide a background magnetic field. This field acts as an analog to emulate the magnetic field of the interplanetary medium (IM), which is the result of the Parker Spiral.

A compact torus injector (CTI) mounted at −5° latitude and 150° longitude supplies the scaled ICME for this experiment. Figure 3(c) shows a cross section diagram displaying the function. In short, the CTI works similarly to a rail gun. The CTI is filled with plasma, then current flows through the outer conductor, and arcs flow through the plasma and to the center electrode to create a toroidal magnetic field. The magnetic pressure forces the plasma toward the end, and as the plasma passes the end of the center electrode, the field reconnects, and the plasma detaches, creating a compact torus (CT) with a flux rope magnetic field structure confining the plasma. This CT generates the shock that we measure in the experiment. A more detailed description of the CTI is found in the study by Endrizzi.19 

In the experiment, we used three main diagnostics: the Hook probe, the Speed probe, and the Te probe. The Hook probe, installed at −10° latitude and 135° longitude, is a Bdot probe array that has 15 individual Bdot probes for diagnosing changes in magnetic field in three orthogonal directions. The defining feature of the Hook probe is that it has a 90° bend in it, which allows for diagnosing a cross section of the experiment. The Speed probe, installed at 0° latitude and −30° longitude, is a Bdot probe array composed of 16 individual Bdot probes. The Speed probe is a straight probe that is positioned along the direction of travel for our scaled ICME. This way, any magnetic disturbances caused by the scaled ICME will propagate along the length of the probe and can be traced back in space and in time, inferring the speed, hence the name. The T e probe, installed at 5° latitude and 135° longitude, is a Langmuir probe with a variable insertion length that is used to measure density and temperature in the experiment.

We used our setup to fire 406 shots during the course of the experiment; however, various errors in some individual shots resulted in unusual and unusable data. That, in addition to several calibration shots, resulted in only around 250 shots for analysis. We use the Speed probe's data to track the time and position of the first magnetic disturbance (i.e., the shock). Figure 4 shows the times when the shock passes each individual sensor of the Speed probe. Since the sensors have known positions, we divide the change in position by the change in time to get velocity. This is a design and technique used in previous BRB studies.21,22 For average velocity, we divide the change in position by the change in time for the disturbance between the first and last sensors. In this, we find that the average speeds of the CTs lie between 96 and 160 km/s with error for each speed measurement of ±15 km/s. The error is introduced by the spatial distance between the sensors and the frequency of data collection.

FIG. 4.

Example of speed calculations from an individual shot. The y axis is the radial position inside the BRB. The position value crossing zero is representative of being on the other side of the BRB vessel. The shock forms immediately after the CTI launches the CT that occurs at around 18.02 ms. The analog-to-digital converters (digitizers) used in the experiment collect data at a rate of 1 MHz, so the temporal error is around 0.5 μs. The sensors of the Speed probe are spaced 5.3 cm apart, so the spatial error is around 2.5 cm.

FIG. 4.

Example of speed calculations from an individual shot. The y axis is the radial position inside the BRB. The position value crossing zero is representative of being on the other side of the BRB vessel. The shock forms immediately after the CTI launches the CT that occurs at around 18.02 ms. The analog-to-digital converters (digitizers) used in the experiment collect data at a rate of 1 MHz, so the temporal error is around 0.5 μs. The sensors of the Speed probe are spaced 5.3 cm apart, so the spatial error is around 2.5 cm.

Close modal

We use the Hook probe to obtain a cross-sectional view of the magnetic structure of the experiment. Since the Bdot probes used in this experiment only measure d B ( t ) / d t , we performed numerical integration to obtain B(t). The Hook probe, as well as the other probes used in this experiment, has noise values around three orders of magnitude smaller than peak signal values. To maintain accuracy during the integration and to get rid of noise, we averaged over a short period of time during data collection before the CT was fired and then subtracted this value from the data before performing a cumulative trapezoidal integration using an in-house Python code. Doing this for all of the sensors yields a two-dimensional (2D) plot that yields the magnetic field strengths at different positions along the probe as a function of time. Figures 5(b) and 5(c) show that we used this method for the z ̂ direction for both the Hook probe and the Speed probe, while Fig. 5(a) provides an example of a lineout from a single sensor on the Hook probe. In Fig. 5(b), “axial position” refers to the z ̂ position inside the BRB, with 0 being the center plane of the machine, denoting the “equator.” The z ̂ coordinate of the magnetic field is most important to us because it is the direction of the applied magnetic field. It is also important to note that the 2D plots are made for visual simplicity, and “stair stepping” effects shown in Fig. 5(c) are not physical and due to the discrete measurements of the probe array.

FIG. 5.

Data from the Hook and Speed probes. (a) A lineout from a single sensor from the Hook probe. (b) The ensemble of sensors from the Hook probe with the red box indicating which probe is displayed in the lineout. (c) The ensemble of sensors from the Speed probe. For all three graphs, the time value of 0 is the moment that the digitizers begin to record data. System noise before 18 ms is associated with triggering the capacitors but prior to the CT being injected.

FIG. 5.

Data from the Hook and Speed probes. (a) A lineout from a single sensor from the Hook probe. (b) The ensemble of sensors from the Hook probe with the red box indicating which probe is displayed in the lineout. (c) The ensemble of sensors from the Speed probe. For all three graphs, the time value of 0 is the moment that the digitizers begin to record data. System noise before 18 ms is associated with triggering the capacitors but prior to the CT being injected.

Close modal

In the magnetic field lineouts from the Hook probe, starting around 18 ms after the initialization of the shot, there is a clear and sharp spike in the magnetic field, jumping from 20 to 40 G, an indicator of a shock. Immediately following the shock, the magnetic field decreases and exhibits structure, which is a common feature of the sheath behind a shock. After the sheath, the magnetic field becomes smooth before returning to the background magnetic field, evidence of the CT finally passing.

In the T e probe data, the same regions: shock, sheath, and ejecta are distinguishable. The temperature goes from a background of 13 to over 50 eV, and the electron density goes from around 6 × 1011 up to 1 × 10 12 cm 3 , identifying the shock. After the shock, both the temperature and the density fluctuate rapidly before gaining structure afterward, which is evidence of the sheath and ejecta, respectively. Figure 6 plots a single lineout of data from the Hook probe with temperature and density, allowing us to see how they change together. Since the probes are in different places spatially, the CT will have different arrival times for the different probes. We correct for this by aligning the shock position when plotting data from the Hook probe with data from the T e probe. The shock is identified qualitatively by the front edge of the initial spike in the data. Table I shows measured variables of the CT and background that are used in calculating the dimensionless scaling parameters.

FIG. 6.

Plot showing temperature with density and magnetic field all normalized by their ambient conditions. Variables with the subscript “a” represent the values before the launch of the CT. The flat part of the temperature line is an artifact of data collection and not probe saturation. The time axis in this graph starts at 17.95 ms for the same reason the graphs in Fig. 5 begin at 18 ms, to cut out system noise and uninteresting data.

FIG. 6.

Plot showing temperature with density and magnetic field all normalized by their ambient conditions. Variables with the subscript “a” represent the values before the launch of the CT. The flat part of the temperature line is an artifact of data collection and not probe saturation. The time axis in this graph starts at 17.95 ms for the same reason the graphs in Fig. 5 begin at 18 ms, to cut out system noise and uninteresting data.

Close modal
TABLE I.

Measured values used in calculating dimensionless scaling parameters. The parameters measured are the electron temperature, Te, density, n, and magnetic field, B, of both the background and the CT itself. These are used in calculating the respective thermal and magnetic pressures.

Parameter Expression Value Unit
Background plasma       
Electron temperature  Te  13.3 ± 0.11  eV 
Density  n  (5.8 ± 0.06)  × 10 11   cm−3 
B field  B  20 ± 0.01 
Thermal pressure  nkTe  1.23 ± 0.02  J/m−3 
Magnetic pressure  B 2 / 2 μ 0   1.59  ±  4.0 × 10 7   J/m−3 
Sound speed  cs  46 105 ± 191  m/s 
Alfvén speed  vA  19 354 ± 28.9  m/s 
Compact torus       
Electron temperature  Te  40 ± 0.13  eV 
Density  n  (3.5 ± 0.05)  × 10 12   cm−3 
B field  B  5 ± 0.23 
Thermal pressure  nkTe  22.4 ± 0.33  J/m−3 
Magnetic pressure  B 2 / 2 μ 0   0.01 ± 2.1  × 10 4   J/m−3 
Parameter Expression Value Unit
Background plasma       
Electron temperature  Te  13.3 ± 0.11  eV 
Density  n  (5.8 ± 0.06)  × 10 11   cm−3 
B field  B  20 ± 0.01 
Thermal pressure  nkTe  1.23 ± 0.02  J/m−3 
Magnetic pressure  B 2 / 2 μ 0   1.59  ±  4.0 × 10 7   J/m−3 
Sound speed  cs  46 105 ± 191  m/s 
Alfvén speed  vA  19 354 ± 28.9  m/s 
Compact torus       
Electron temperature  Te  40 ± 0.13  eV 
Density  n  (3.5 ± 0.05)  × 10 12   cm−3 
B field  B  5 ± 0.23 
Thermal pressure  nkTe  22.4 ± 0.33  J/m−3 
Magnetic pressure  B 2 / 2 μ 0   0.01 ± 2.1  × 10 4   J/m−3 

The results of the experiment are promising, as we have evidence of the three main sections of an ICME. However, we must compare to our scaling arguments. Calculating the dimensionless numbers with our experimental values shown in Table I, we get a plasma β = 0.77 ± 0.01. Thus, for the reasons laid out in Sec. II, we can argue that our experiment is well scaled in that regard. Furthermore, we can use the values from Table I to calculate the total pressure ratio for our experiment. Taking the temperature of the inside of the ejecta to be 40 ± 0.13 eV and at (3.5 ± 0.05)  × 10 12  cm 3 , we get P ratio ∼7.9 ± 0.05, which is well in the range of our requirements. Doing similar calculations for our scaling of the magnetosonic Mach number and plasma β yields the values shown in Table II.

TABLE II.

Key dimensionless numbers used in scaling the experiment. These values were calculated using the values given in Table I.

Parameter Symbol ICME/IM Experiment
Magnetosonic Mach number  M ms   1.6  2.3 ± 0.3 
Plasma beta in background  β  1.0  0.77 ± 0.01 
Total pressure ratio  P ratio   7.9 ± 0.05 
Parameter Symbol ICME/IM Experiment
Magnetosonic Mach number  M ms   1.6  2.3 ± 0.3 
Plasma beta in background  β  1.0  0.77 ± 0.01 
Total pressure ratio  P ratio   7.9 ± 0.05 

In a collisional shock, we expect the front to be a few collisional mean free paths thick.23 From the background plasma, we calculate λ i 6  m. The temporal width of the shock we measure is of the order of 3 μs, and factoring the average speed of the shock of 150 km/s yields a shock thickness (Ls) of 45 cm. We can then see that λ i / L s > 1 , which suggests that the shock cannot be sourced by collisions.

An interesting result comes with the measuring of the speed of the shock. In Fig. 4, an x2 fit is used to more closely match the data. This implies that the speed of the shock changes, especially toward the beginning before the velocity becomes more constant later in time. This may be caused by a density gradient in the background plasma of the BRB, assuming the plasma guns did not uniformly distribute plasma throughout the vessel before injecting the CT, or may also be due to the expansion of the CT plasma.

ICME events are important to study in controlled environments because knowing how they evolve helps us mitigate the impact of more powerful ICMEs. To study them, we injected a compact torus into a background plasma perpendicular to a magnetic field in the BRB at the WiPPL. To ensure our experiment is well scaled, we control the plasma β, P tot , and c ms of the background plasma. We diagnosed the experiment directly using magnetic field and temperature probes. With these, we measured the speed of the shock caused by our scaled ICME, as well as the magnetic field, temperature, and density as a function of time. We find that the speeds of the shock range from 100 to 200 km/s and used the time-resolved data to identify different features of the scaled ICME, including the shock, sheath, and ejecta. We calculated our dimensionless numbers and find our background plasma with a β of 1.3 ± 0.1, the magnetosonic Mach number of our scaled ICME to be around 2, and the total pressure ratio inside the ejecta to the background to be 7.9 ± 0.1 as laid out in Table II. The uncertainties of our values are obtained by the instrumental errors added in quadrature. These dimensionless numbers satisfy our scaling requirements and, therefore, argue that the experiment is well scaled.

The data in this paper are promising; however, it is meant to complement other methods of studying ICMEs, not replace them. The fact that the compact torus is launched “face on,” whereas an ICME is typically measured as approaching “edge on” impacts the parity between systems. Also, while the scaling parameters may provide similar effects to that of an ICME, there can be kinetic effects taking place in the shock formation and propagation that may vary in timescale and strength not covered by the parameters in this paper. This experiment provides an approximation of an ICME using laboratory equipment and is not enough to replace observation or simulation of ICME events.

These results open the door to further research into ICMEs. This first step in creating a scaled ICME allows us to gather a lot more information regarding how they evolve and interact with different obstacles or fields. This first experiment serves as a proof of concept that we can create a scaled ICME. The next experiment in this project will focus on a CT's interactions with a gradient magnetic field. Future papers will include a deeper dive into the changes that the CT undergoes as it travels through the BRB as detected by the Speed probe.

This work is funded by the U.S. Department of Energy, Fusion Energy Sciences, under Award No. DE-SC0021288. The WiPPL Collaborative Research Facility is supported through the US Department of Energy grant DE-SC0018266. This research collaboration was established and maintained as part of the MagNetUS ecosystem.

The authors have no conflicts to disclose.

K. Bryant: Formal analysis (lead); Investigation (equal); Writing – original draft (lead); Writing – review & editing (equal). R. P. Young: Conceptualization (equal); Funding acquisition (lead); Investigation (supporting); Writing – review & editing (equal). H. J. LeFevre: Funding acquisition (supporting); Supervision (equal); Writing – review & editing (equal). C. C. Kuranz: Conceptualization (equal); Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal). J. R. Olson: Investigation (equal); Supervision (lead); Writing – review & editing (equal). K. J. McCollam: Resources (equal); Supervision (equal); Writing – review & editing (equal). C. B. Forest: Funding acquisition (equal); Resources (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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