A magnetic levitation based low-gravity simulator with an unprecedented large functional volume 1,2 1,2, Hamid Sanavandi and Wei Guo ∗ 1National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, USA 2Mechanical Engineering Department, FAMU-FSU College of Engineering, Florida State University, Tallahassee, Florida 32310, USA (Dated: August 3, 2021) Low gravity environment can have a profound impact on the behaviors of biological systems, the dynamics and heat transfer of fluids, and the growth and self-organization of materials. Systematic research on the effects of gravity is crucial for advancing our knowledge and for the success of space missions. Due to the high cost and the limitations in the payload size and mass in typical spaceflight missions, ground-based low-gravity simu- lators have become indispensable for preparing spaceflight experiments and for serving as stand-alone research platforms. Among various simulator systems, the magnetic levitation based simulator (MLS) has received long-lasting interests due to its easily adjustable gravity and practically unlimited operation time. However, a recognized issue with MLSs is their highly non-uniform force field. For a solenoid MLS, the functional volume V1%, where the net force results in an acceleration less than 1% of the Earth’s gravity g, is typically a few micro- liters (µL) or less. In this work, we report an innovative MLS design that integrates a superconducting magnet with a gradient-field Maxwell coil. Through an optimization analysis, we show that an unprecedented V1% of over 4,000 µL can be achieved in a compact coil with a diameter of 8 cm. We also discuss how such an MLS can be made using existing high-Tc superconducting materials. When the current in this MLS is reduced to emulate the gravity on Mars (gM = 0.38g), a functional volume where the gravity varies within a few percent of gM can exceed 20,000 µL. Our design may break new ground for various exciting future low-gravity research. INTRODUCTION ets [23], and suborbital rocketry [24]. Despite their useful- ness, a known limitation of these facilities is the relatively Reduced gravity is known to have important effects on vari- short low-gravity duration (i.e., from several seconds to a few ous biological and physical systems. For instance, a weight- minutes [25]), which makes them unsuitable for experiments less environmentmay prohibitcell culture growth [1] and may that require long observation times [26]. In biological and cause cellular stressor and bone loss that can negatively im- medical research, rotational facilities such as clinostat ma- pact astronauts’ health [2–4]. In fluid systems, reduced grav- chines [27, 28], rotating wall vessels [29], and random po- ity can significantly affect the sloshing dynamics of cryogenic sitioning machines [30] are also adopted to achieve a small propellants in spacecrafts [5], the surface oscillation of liq- time-averaged gravity vector [31, 32]. Although these sim- uid drops [6], bubble cavitation [7] and boiling heat transfer ulators are convenient, they do not produce a genuine low- in fluids [8, 9]. In material science, the potential of reduced gravity environment and can generate unwanted centrifugal gravity in growing tissues [10] and crystals [11] and for ma- forces and circulating flows in the samples [31–33]. terials processing [12] has been recognized. Conducting sys- On the other hand, magnetic field-gradient levitation of var- tematic research to understand the mechanism of gravity in ious diamagnetic materials has been demonstrated [34–36]. these diverse systems will undoubtedly advance our knowl- Even living organisms have been successfully levitated [37– edge. Furthermore, various programs initiated recently by 41], and there is no evidence of any cumulative harmful ef- public space agencies and private organizations [13–15] aim- fects due to the field exposure [40–42]. Compared to other ing at long-term human habitation of the Moon and Mars have low-gravity simulator systems, a magnetic levitation based further strengthened the needs of experimental research in low simulator (MLS) offers unique advantages, including low gravity environment. cost, easy accessibility, adjustable gravity, and practically un- The ideal microgravity condition can be achieved in limited operation time [37, 38, 43]. However, a known is- spaceflight experiments conducted during space-shuttle mis- sue with MLSs is their highly non-uniform force field around arXiv:2108.00520v1 [physics.space-ph] 1 Aug 2021 sions [16] and at space stations [17]. However, these experi- the levitation point. If we define a 0.01-g functional volume ments are limited by the high cost and the small payload size V1% where the net force results in an acceleration less than and mass [18]. The fact that the astronauts have to conduct 1% of the Earth’s gravity g, V1% is typically less than a few the experiments instead of the trained scientists also put con- microlitres (µL) for conventional solenoid MLSs. Although straints on the design of the experiments. For these reasons, diamagnetic samples with sizes larger than V1% can be lev- researchers have devoted great efforts in developing ground- itated, a stress field caused by the residue force inside the based low-gravity simulators. One major category, which samples can compromise the measurement results. Despite utilizes free fall to generate near-zero gravity, includes drop some limited efforts in designing MLSs for improved func- towers [19, 20], parabolic aircrafts [21, 22], sounding rock- tional volumes [44–46], a major progress is still lacking. Fur- thermore, the high energy consumption rate of conventional resistive solenoid MLSs is also concerning. For instance, 4 MW electric power is required to levitate a frog using a resis- ∗ Corresponding author: [email protected] tive solenoid MLS [37]. 2 In this paper, we report an innovative MLS design which consists of a gradient-field Maxwell coil placed in the bore of a superconducting (SC) magnet. By optimizing the SC magnet’s field strength and the current in the Maxwell coil, we show that an unprecedented V1% of over 4,000 µL can be achieved in a compact coil of 8 cm in diameter. This optimum V1% increases with the size and the field strength of the MLS. We then discuss how such a MLS can be made using existing high-Tc superconducting materials so that long-time operation with minimal energy consumption can be achieved. To further demonstrate the usefulness of this MLS, we also consider re- ducing its current and the field strength to emulate the gravity on Mars (gM = 0.38g). It turns out that a functional volume over 20,000 µL can be produced, in which the gravity only varies within a few percent of gM. Our design concept may break new ground for exciting applications of MLSs in future low-gravity research. RESULTS To aid the discussion of our MLS design, we first introducethe fundamentals of magnetic levitation using a solenoid magnet. Following this discussion, we will present the details of our innovative MLS design concept. Levitation by a solenoid magnet FIG. 1. (a) Schematic of a solenoid with a diameter of D = 8 cm and a height of √3D/2. (b) Calculated specific potential energy E(r) of The concept of magnetic levitation can be understood by con- a small water sample placed in the magnetic field. The turn-current sidering a small sample (volume ∆V) placed in a static mag- NI of the solenoid is 607.5 kA. The origin of the coordinates is at the netic field B(r). Due to the magnetization of the sample ma- center of the solenoid. The dashed contour denotes the boundary of terial, the energy of the magnetic field increases by [47] the trapping region, and the solid contour shows the low-force region (i.e., acceleration less than 0.01g). (c) The functional volume V1% (i.e., overlapping volume of the two contours) versus the turn-current χB2(r) ∆EB = − ∆V, (1) NI. Representative shapes of the low-force region are shown. 2µ0(1 + χ) where χ is the magnetic susceptibility of the sample material and µ0 is the vacuum permeability. For diamagnetic materials In order to attain a stable levitation, the specific potential with negative χ, ∆EB is positive and therefore it requires en- energy E must have a local minimum at the levitation point so ergy to insert a diamagnetic sample into the B(r) field. Count- the sample cannot stray away. Since E depends on the mate- ing in the gravity effect, the total potential energy associated rial properties besides the B(r) field, we need to specify the with the sample per unit volume can be written as: sample material. Considering the fact that water has been uti- lized in a wide range of low-gravity researches [48–50] and is χB2(r) also the main constituent of living cells and organisms [51], E(r)= − + ρgz, (2) 2µ0(1 + χ) we adopt the water properties at ambient temperature [52] 6 3 3 (i.e., χ = 9.1 10− and ρ = 10 kg/m ) in all subsequent where ρ is the material density and z denotes the vertical co- analyses.− To see× the effect of the B(r) field, we consider an ordinate. This energy leads to a force per unit volume acting solenoid with a diameter of D = 8 cm anda heightof √3D/2, on the sample as: as shown in Fig. 1 (a). These dimensions are chosen to match χ the size of the MLS that we will discuss in later sections. For a F = ∇E(r)= B ∇B ρgeˆz. (3) solenoid with N turns and with an applied current I, B(r) can µ (1 + χ) − 0 · − be calculated using a known integral formula that depends on For an appropriate non-uniform magnetic field, the vertical the product NI (see details in the Method section).