to their great mobility and large numbers. Current in the arc is sustained by thermionic emission and field emission of electrons at the cathode. The current may be concentrated in a very small hot spot on the cathode; current densities on the order of one million amperes per square centimeter can be found. Unlike a glow discharge, an arc has little discernible structure, since the positive column is quite bright and extends nearly to the electrodes on both ends. The cathode fall and anode fall of a few volts occur within a fraction of a millimeter of each electrode. The positive column has a lower voltage gradient and may be absent in very short arcs. A low-frequency (less than 100 Hz) alternating current arc resembles a direct current arc; on each cycle, the arc is initiated by breakdown, and the electrodes interchange roles, as anode or cathode, when current reverses. As the frequency of the current increases, there is not enough time for all ionization to disperse on each half cycle, and the breakdown is no longer needed to sustain the arc; the voltage vs. current characteristic becomes more nearly ohmic. The various shapes of electric arcs are emergent properties of non-linear patterns of current and electric field. The arc occurs in the gas-filled space between two conductive electrodes (often made of tungsten or carbon) and it results in a very high temperature, capable of melting or vaporizing most materials. An electric arc is a continuous discharge, while the similar electric spark discharge is momentary. An electric arc may occur either in direct current (DC) circuits or in alternating current (AC) circuits. In the latter case, the arc may re-strike on each half cycle of the current. An electric arc differs from a glow discharge in that the current density is quite high, and the voltage drop within the arc is low; at the cathode, the current density can be as high as one megaampere per square centimeter. An electric arc has a non-linear relationship between current and voltage. Once the arc is established (either by progression from a glow discharge or by momentarily touching the electrodes then separating them), increased current results in a lower voltage between the arc terminals. This negative resistance effect requires that some positive form of impedance (as an electrical ballast) be placed in the circuit to maintain a stable arc. This property is the