# Coupled System of Dual-Axis Clinostat and Helmholtz Cage for Simulated Microgravity Experiments
## 2 Design and Construction
### The Helmholtz Cage  
The constructed Helmholtz cage is a device that can modify the magnetic field inside its central part, where the clinostat can be located. The cage is built from three pairs of octagonal coils, with the biggest one inscribed in a circle of diameter 2 m; the other two pairs of coils are slightly smaller, to be mounted inside the largest coils. 90 turns per coil were wound on alumina skeletons using 1.2 mm diameter copper wire. The octagonal  
Figure 9: Electric diagram of LEDs’ control and electric supply of the lighting system. The optotransistor PC817 controls the MOSFET IRF540N gate.  
coil shape was chosen because of its induction properties being very close to those of a circle, while the mechanical construction is simple enough. It is worth mentioning that in the simplest case, square cages are commonly used [40; 41; 42], but they have limited magnetic-field homogeneity.  
The cage is powered with three Rigol(r) (Suzhou, China) DP811 variable power supplies (Figure 10). Each supply powers one Helmholtz coil pair. The maximum power that can be delivered to one pair of coils equals 100 W (20 V, 5 A).  
To find the magnetic-field spatial distribution inside the cage, adequate calculations, on the base of [PERSON]'s law using a custom-made Python code, were performed. The imposed condition of about 1% deviation from the field value in the cage center (located 1 m above the construction base) resulted in the determination of the optimum experimental region of homogeneity. In Figures 11 and 12, the results of simulations are presented for different numbers N of hypothetical coil polygon sides (we used N = 8). The simulation was further validated with measurements inside the built Helmholtz cage.  
Figure 11: Results of simulation of magnetic-induction spatial distribution at the vertical main cross-section of the Helmholtz cage. In the real construction, the N = 8 case was chosen and the distances from the center of Helmholtz cage were equal to +/\(-\)492 mm, +/\(-\)471 mm, +/\(-\)440 mm.  
Figure 10: Block diagram of the control signal flow for the Helmholtz cage.  
As mentioned earlier, the clinostat and the Helmholtz cage were designed to be complementary, in the sense that they are dimensionally compatible (Figure 13)--the center point of the cultivation sphere is identical to the middle of the cage. Importantly, the diameter of the sphere is comparable with the previously simulated region (0.4 m \(\times\) 0.4 m \(\times\) 0.4 m), possessing adequate field homogeneity.  
We did not assume rapid changes of Earth magnetic field during experiments. Using simulations and direct measurements, at the initial phase of the experiment, we are able to find such conditions in which the Earth magnetic field is compensated. In the laboratory, we did not notice any long-term fluctuations of the field. Looking at Figure 12, the magnetic field's spatial uniformity in the central region of the cage is better than 2%. For a typical value of the magnetic-field induction equal to about 45 uT, the 2% time fluctuations of the field are equivalent to about 0.9 uT. It can be assumed that the presented setup will work with such accuracy in the static-field mode. However, for future long-time experiments, the system should be updated to closed-loop active-field compensation.  
Figure 12: (**a**) Results of simulations and (**b**) the measured magnetic-field values inside the central region of the Helmholtz cage. The measurements were carried out with the AlphaLab Milligauss MR3 magnetometer.  
Figure 13: The general view of the experimental system. Inside the Helmholtz cage, the clinostat is placed.