Carbon rods made for carbon arcs are available at some welding supply stores. These carbon rods often have a copper jacket to improve conductivity. The copper melts away from the tips of the carbon rods, exposing a short portion of the carbon rod. Do not connect an arc directly to a power source. Something must be in series with it to limit current.
Most arcs have a slightly nasty characteristic, becoming greatly more conductive as they get hotter.
This is used as a resistor. To start the arc, the power is turned on with the carbon rods separated. The carbon arc itself is fairly bright, but the tips of the carbon rods are usually much brighter. The tips of the carbon rods get heated up to a temperature usually near 3600 degrees Celsius, or approx. 6500 degrees Fahrenheit.