A high vacuum will also break down under a sufficiently high DC field. Under an increasing DC voltage, small projections on the negative electrode (called "asperities") begin to experience a localized electric field that is sufficient to initiate field emission, often accompanied by intense localized heating, thermoelectric emission, or even explosive emission of electrons and ejection of cathode material into the gap. Field emission is a function of the cathode material's Work Function - i.e., how easy electrons can be stripped from the cathode. Each of these events generates a microplasma at the site of the asperity, and electrically, each event shows up as a small spike of current through the gap. Under somewhat higher voltages, one of these events may culminate in a spark that completely bridges the gap. If driven from a low impedance source, the spark may evolve into a sustained vacuum arc. Vacuum arcs often cause significant heating and surface melting of the anode as well as the cathode.
A high voltage vacuum gap (as in a transmitting vacuum tube cathode-anode, vacuum capacitor, or vacuum switch) can be "conditioned" to operate at higher voltages by using an adjustable HV supply, current limiting resistor, and a small capacitor. Any asperities are melted or vaporized by the controlled energy in the HV capacitor, but damaging arcing is prevented by the resistor. The high voltage is slowly increased until the gap can operate at maximum voltage without further breakdown. This process is also called "spot knocking".
Although the mechanisms are different, both air gaps and vacuum gaps may show pre-breakdown current pulses. And, once spark breakdown or arcing occurs, the negative resistance VI characteristics are also similar for gaseous and vacuum sparks and arcs. However, when current flow is temporarily stopped (as during a current zero-crossing in an AC circuit), a vacuum arc will usually recover its dielectric strength more quickly than an arc within a gas.
A good discussion can be found in, "Initiation of electrical breakdown in vacuum" by R.V. Latham, 1978 Physics in Technology 9 20-5, DOI: 10.1088/0305-4624/9/1/I02