Streamer or Kanal Mechanism of Spark

STREAMER OR KANAL MECHANISM OF SPARK

We know that the charges in between the electrodes separated by a distance d increase by a factor e^αd when field between electrodes is uniform. This is valid only if we assume that the field E₀ = V/d is not affected by the space charges of electrons and positive ions. Raether has observed that if the charge concentration is higher than 10⁶ but lower than 10⁸ the growth of an avalanche is weakened i.e., dn/dx < e^αd.

Whenever the concentration exceeds 10⁸, the avalanche current is followed by steep rise in current and breakdown of the gap takes place. The weakening of the avalanche at lower concentration and rapid growth of avalanche at higher concentration have been attributed to the modification of the electric field E₀ due to the space charge field. Fig. 2.6 shows the electric field around an avalanche as it progresses along the gap and the resultant field i.e., the superposition of the space charge field and the original field E₀. Since the electrons have higher mobility, the space charge at the head of the avalanche is considered to be negative and is assumed to be concentrated within a spherical volume. It can be seen from Fig. 2.6 that the filed at the head of the avalanche is strengthened.

The field between the two assumed charge centres i.e., the electrons and positive ions is decreased as the field due to the charge centres opposes the main field E₀ and again the field between the positive space charge centre and the cathode is strengthened as the space charge field aids the main field E₀ in this region. It has been observed that if the charge carrier number exceeds 10⁶, the field distortion becomes noticeable. If the distortion of field is of 1%, it would lead to a doubling of the avalanche but as the field distortion is only near the head of the avalanche, it does not have significance on the discharge phenomenon. However, if the charge carrier exceeds 10⁸, the space charge field becomes almost of the same magnitude as the main field E₀ and hence it may lead to initiation of a streamer. The space charge field, therefore, plays a very important role in the mechanism of electric discharge in a non-uniform gap.

Townsend suggested that the electric spark discharge is due to the ionization of gas molecule by the electron impact and release of electrons from cathode due to positive ion bombardment at the cathode. According to this theory, the formative time lag of the spark should be at best equal to the electron transit time t_r. At pressures around atmospheric and above p.d. > 10³ Torr-cm, the experimentally determined time lags have been found to be much shorter than t_r. Study of the photographs of the avalanche development has also shown that under certain conditions, the space charge developed in an avalanche is capable of transforming the avalanche into channels of ionization known as streamers that lead to rapid development of breakdown. It has also been observed through measurement that the transformation from avalanche to streamer generally takes place when the charge within the avalanche head reaches a critical value of

n₀e^αx ≈ 10⁸ or αX_c ≈ 18 to 20

where Xc is the length of the avalanche parth in field direction when it reaches the critical size. If the gap length d < Xc, the initiation of streamer is unlikely.

The short-time lags associated with the discharge development led Raether and independently Meek and Meek and Loeb to the advancement of the theory of streamer of Kanal mechanism for spark formation, in which the secondary mechanism results from photo ionization of gas molecules and is independent of the electrodes.

Raether and Meek have proposed that when the avalanche in the gap reaches a certain critical size the combined space charge field and externally applied field E₀ lead to intense ionization and excitation of the gas particles in front of the avalanche head. There is recombination of electrons and positive ion resulting in generation of photons and these photons in turn generate secondary electrons by the photo ionization process. These electrons under the influence of the electric field develop into secondary avalanches as shown in Fig. 2.9. Since photons travel with velocity of light, the process leads to a rapid development of conduction channel across the gap.

Raether after thorough experimental investigation developed an empirical relation for the streamer spark criterion of the form

where E_r is the radial field due to space charge and E₀ is the externally applied field. Now for transformation of avalanche into a streamer E_r ≈ E

Therefore, αx_c = 17.7 + ln x_c

For a uniform field gap, breakdown voltage through streamer mechanism is obtained on the assumption that the transition from avalanche to streamer occurs when the avalanche has just crossed the gap. The equation above, therefore, becomes

αd = 17.7 + ln d

When the critical length X_c ≥ d minimum breakdown by streamer mechanism is brought about.

The condition X_c = d gives the smallest value of α to produce streamer breakdown.

Meek suggested that the transition from avalanche to streamer takes place when the radial field about the positive space charge in an electron avalanche attains a value of the order of the externally applied field. He showed that the value of the radial field can be obtained by using the expression.

where x is the distance in cm which the avalanche has progressed, p the gas pressure in Torr and  α   the Townsend coefficient of ionization by electrons corresponding to the applied field E. The minimum breakdown voltage is assumed to correspond to the condition when the avalanche has crossed the gap of length d and the space charge field E_r approaches the externally applied field i.e., at x = d, E_r = E. Substituting these values in the above equation, we have

The experimentally determined values of α/p and the corresponding E/p are used to solve the above equation using trial and error method. Values of α/p corresponding to E/p at a given pressure are chosen until the equation is satisfied.