AZIRIDINATION USING N-TOSYLOXYCARBAMATES

In an extensive corona, having many branches over a length of several tens of cen-timetres, the number of electrons able to reach the stem of the streamer trails at the point of origin, close to the anode, becomes considerable. Extensive detachment of electrons from negative ions in that region is also believed to occur. As a result of energy exchange between the energetic electrons and neutral gas molecules, the rate of ohmic loss of energy increases and significant heating of the channel can occur.

The temperature of the neutral gas thus rises, as a result of which it expands; the gas density falls. The quantity E/N therefore increases and ionisation becomes more efficient. The process is cumulative and a transition takes place to a highly ionised arc-like channel of high temperature and relatively high conductivity. The channel has now been transformed into a leader which proceeds to grow in the general direction of the electric field.

An idealised model of leader development is given in Figure 1.6, in which a rod–

rod gap is imagined to be subjected to an impulse voltage with a time to peak of the order of a few hundred microseconds. The voltage at the positive electrode rises until the field at the tip exceeds 3× 10⁶Vm⁻¹at time t₁when a streamer corona forms. A burst of current is detected in the circuit. The corona injects a net positive charge into the region, so reducing the field at the tip and inhibiting further streamer formation for a ‘dark’ period until the voltage has increased. A second corona (often termed a secondary corona) then occurs at time t₂which may be followed by others at short intervals of time thereafter (omitted for clarity). After another corona is formed, at t₃, sufficient heating has occurred in the streamer stem at the anode for a leader channel to form. Where the diameter of the electrode is relatively large, the leader may form immediately out of the secondary corona at time t₂. In either case, it extends in length across the gap towards the opposite electrode. Since the leader channel is highly conducting the potential of its tip remains high and a streamer corona forms ahead. Thus, the avalanches at the heads of the streamers provide the ionisation and, therefore, the electron current and consequent heating needed for further leader development.

The streamer coronas have formed more or less continuously as the leader has extended across the gap. Since the positive ions deposited remain immobile on the timescale involved, a roughly cylindrical volume of remanent positive charge surrounds the leader channel along the whole of its length.

250 t,μs

τ

t₄ t₁ +

–

t₂ t₃

U_cr

U,kV

Figure 1.6 Simplified picture of streamer and leader development to breakdown in a rod–rod gap under an impulse voltage rising to peak in 250 μs When the field at the negative electrode exceeds the order of (5–6)× 10⁶Vm⁻¹ at time t4negative streamers (section 1.2.9) can form and develop towards the anode, but, as these require an ambient field of about 10⁶Vm⁻¹to progress, they do not extend as far into the gap as do the positive streamers. Moreover, by contrast with the process at the positive electrode, the electrons are moving into a reducing electric field. At a later stage, transformation to a leader occurs but these processes occur at higher fields than is the case with the positive counterparts, and the distance traversed is smaller. When the two leader systems meet, a conducting channel bridges the gap and a low voltage arc can complete the breakdown of the gap.

A simple semiempirical argument can be used to relate the streamer and leader lengths and the respective average electric gradients needed for their propagation to the sparkover voltage Vsof the gap. For at the instant at which the systems meet, τ₄, we can write down the sum of the voltages across the gap:

V_s = E_s⁺L⁺_s + E⁺_l L⁺_l + E_s⁻L⁻_s + E_l⁻L⁻_l (1.12) where E_s⁺, E_s⁻, E_l⁺and E⁻_l are the gradients for the positive and negative streamers and leaders, and L⁺_s , L⁻_s , L⁺_l and L⁻_l are the corresponding lengths. Note also that the gap length d is:

d= L⁺s + L⁺_l + L⁻s + L⁻_l (1.13)

Certain of these quantities, such as E_s⁺, E_s⁻are known from independent measure-ments and, in specific experimeasure-ments, lengths of streamers and leaders estimated, so that other quantities in Equation (1.12) can be estimated from a sparkover measurement.

It may be expected from the foregoing descriptions that only a relatively large streamer corona is likely to develop into a leader, where fields near the positive

Figure 1.7 Photograph of leaders developing in a 4 m rod–rod gap [38]. Note that the leader does not develop along the line of maximum field between the rods; also bifurcation at the tip of the rod

electrode are high, detachment of electrons is rapid and large numbers of electrons are found in that region. Thus, leader initiation will occur most readily in large gaps, usually 0.5 m or more, where the sparkover voltage is high. Indeed, Reference 36 shows that the charge in the initial streamer corona, which subsequently produces a leader in a five metre gap, is several tens of microcoulombs.

The description of leader growth in Figure 1.6 is much simplified. For example, the leader rarely follows the axial path between electrodes. It tends to go off-axis in a path which may be much longer than the direct one, particularly if the electrode diameter is relatively large. Moreover, a bifurcation often occurs, originating at the electrode, although one of the two branches is usually dominant. An example of a leader in a long gap is shown in Figure 1.7. Waters [37] gives a more detailed description of leader development under impulse voltage in a practical case. Ross et al. [36], quoting results obtained by the Les Renardieres Group, give an interesting summary of quantities associated with leader development in a 10 m gap under the 50 per cent sparkover impulse voltage. For example, the total energy dissipated during the growth of the leader is about 25 J per metre of its length; the current is taken as 0.6 A, so that if the length of streamers in the leader corona, having a gradient of 500 kVm⁻¹, is 1 m, then the power input to the leader corona is 300 kW. Since the

Figure 1.8 Two examples of leader development in a short (0.6 m) rod–plane gap showing on left, streamer formation (leader corona) at the leader tips.

Impulse voltage∼330 kV (after Hassanzahraee, PhD thesis, University of Leeds, 1989)

system advances at the rate of 2 cmμs⁻¹, then the energy dissipated in the leader corona alone in 1 m of advance is about 15 J. The energy available to heat the leader channel itself is estimated at about 10 Jm⁻¹. As will be shown below, these are average values, indicating general features only, since the potential gradient in the leader varies along its length and the leader corona is also variable.

The simple heating process described above suggests also that leaders can be produced in short gaps provided a sufficiently high electric field can be created at the electrode. This can indeed be achieved by impulse overvolting of a gap; Figure 1.8 shows an example obtained in a gap of 0.4 m, to which an impulse of twice the threshold sparkover voltage was applied.