**2. Theoretical model of the** *J***x***B* **arc jet discharge method**

By applying a steady-state weak magnetic field (*B <sup>0</sup>*= 1 – 5 mT) perpendicular to the dis‐ charge current in the arc discharge, the Lorentz force (*J*x*B* force) causes the ejection of the arc plasma and surrounding gas in the *J*x*B* direction as shown in Fig. 1 [8, 11]. In the 1960s, this force in a pulsed discharge was actively studied in relation to the electric propulsion engine of rockets [12].

(8.0 mm), a carbon cathode (15 mm), a viewing port and a movable calorimetric probe. The reactor is evacuated by a rotary pump to a pressure of less than 10 Pa and then closed. After introducing He gas with *p*(He) = 10 – 80 kPa, discharge starts, where the discharge current is *I <sup>d</sup>*= 20 – 80 A and voltage between the electrodes is *V rod*= 20 - 35 V. At the front and back of the reactor, solenoid coils (20 cm inner diameter) are installed to produce a steady state

Production of Carbon Nanotubes and Carbon Nanoclusters by the JxB Arc-Jet Discharge Method

http://dx.doi.org/10.5772/51964

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When a magnetic field is applied during the discharge, the shape of the arc flame dramati‐ cally changes, and a strong plasma flow in the *J*x*B* direction can be observed. Figures 3(a) and (b) respectively show side views of the arc flames for *B <sup>0</sup>*= 0 and *B <sup>0</sup>*= 2.0 mT, where *p*(He)= 40 kPa and *I <sup>d</sup>*= 80 A. The upper direction is the *J*x*B* direction. By applying a magnetic field, the plasma and the hot gas are ejected in the vertically upward direction. The upward flow of carbon particles can sometimes be clearly observed. By developing a calorimeter [11] in which flowing water absorbs the heat flux, the local heat flux is measured and the results are shown in Figs. 4 (a) and (b) [11]. By increasing the magnetic field, the heat flux is local‐ ized in the upper part of the arc plasma (FWHM value of about 50 mm). Above the arc plas‐

magnetic field of *B <sup>0</sup>*= 0 - 5 mT.

ma, the heat flux monotonically increases.

**Figure 2.** Schematic side view of the arc reactor with a calorimetric probe installed.

**Figure 1.** Schematic diagram of the *J*x*B* arc-jet discharge.

Here, this effect is used to eject sublimated carbon atoms in a selected direction. By control‐ ling the magnetic field, control of the hot gas including the carbon material is possible, and suitable conditions to do hot gas reactions for the production of SWNTs and other carbon clusters can be selected. This method can also reduce the influence of the electrode direction and chamber configuration.

When the discharge current density and applied magnetic field are 50 A/cm2 and 5 mT, re‐ spectively, the Lorentz force causing acceleration of electrons and ions is 0.25 N/cm3 . When the gas pressure and the gas temperature around the arc are 30 kPa and 5000 K, respectively, the mean free path and collision frequency of electrons are about 0.01 mm and 10 GHz, re‐ spectively. Because of this high collision frequency, electrons frequently collide with neutral gas atoms and accelerate them in the *J*x*B* direction, resulting in the ejection of hot gas from the arc region. The acceleration time is related to the electron lifetime in the plasma.
