Thor performance measurements

Background

An eternal debate issue among Tesla coilers has traditionally been Tesla Coil (TC) performance. How to measure it? How to improve it? What is its dependance with the tunable parameters?
The contribute of many authors (and maybe mine too?) has explained in detail the contribute of:

Primary capacitor and inductance
Secondary capacitor and inductance
Coupling between primary and secondary

Their effect on the maximum voltage developed at the secondary (for the looseless case) has been analyzed and the location of the optimal working points described.

The previous analysis has however been limited to a single TC excitation, that is a single charge/discharge cycle of the primary capacitor (i.e. a single "bang"). Every coiler knows that leader elongation requires a sequence of bangs and that the distance reached is much longer than the sparkover distance expected from the theoretical secondary voltage estimation. The physical laws governing this phenomena are still partly unknown, measurement data scarce and dated beginning of last century.

Scope of this investigation

Thor, equipped with the CCPS rev.C, allows for searching an answer to the following questions:

How the leader length grows from bang to bang?
How the bang energy influences performance?
How the bang rate influences performance?
How the quenching quality influences performance?

The scope of this investigation is to provide a series of measurements usable to document the effect of the above mentioned variables. It is beyond the scope of this investigation to attempt an explanation of the underlying physical phenomena.
In several respects the investigation results tend to be more qualitative than quantitative. It is difficult to "document" the quenching time setting or to measure the secondary voltage but, nevertheless, it is interesting to know in what proportion and direction they affect the TC performance.

Measurement strategy

The space where the measurement are performed is a multidimensional discrete space. The variables defining the operational conditions are:

Primary capacitor charging voltage (i.e. bang energy)
Bang frequency (BPS, Bangs Per Second)
Strike target distance
Rotating Spark Gap (RSG) gap clearance

The TC performance is estimated by using two stochastic variables:

Bang sequence length (i.e. number of bangs) needed to strike the target (discrete variable B_n)
Bang energy needed to strike the target (continuous variable B_e)

To understand how each of the (four) operational variables affects the performance, is necessary to keep three of them constant and change only the fourth one. This constrains the measurement space to a zone where this condition (i.e. independence) can be arranged.
In other words, the CCPS can't fully charge the primary capacitor more than 370 times per second, if the RSG rotates below 200 BPS it will re-ignite as the the capacitor starts charging, a voltage below 14 kV hardly triggers the RSG and so on.

Naming conventions

Discharge naming in the literature is usually different from author to author. Tesla coiler usually speak about "streamers". In these pages naming is used as follows:

Streamer(s): very thiny filament(s) that originate in the corona area at the discharge front. They are hardly visible without a camera.
Leader: for distances over a meter, the discharge advances from the starting electrode as a luminous leader growing length. The leader free end carries a streamer bunch. The discharges not very intense but visible that coilers call "streamers" are actually leaders.
Breakdown: when a leader reaches the other electrode, charge is accumulated in the formed channel and its conductivity grows accordingly. The current rises rapidly and the gap "conducts". Light, heat and noise is produced. Coiler talk about "fat streamers". Breakdown is also called final jump in the literature (when breakdown is associated with long gaps). Breakdown always require a target (e.g. a grounded stick, floor, ceiling, etc.).

Measurement setup

On one side of Thor's top toroid a stainless steel sphere has been mounted (diameter 25 mm) in order to provide a preferred spot for the discharges. The target is made with a vertical aluminum pipe, which has its top end bended horizontally for about 200 mm. The pipe is mounted on a pedestal and grounded. An insulator is mounted on the pipe bended end and a 60 mm diameter copper ball terminates the target. The resulting copper ball height from ground is the same than Thor's stainless steel little ball.

A thick shielded cable runs inside of the aluminum pipe. Its central conductor is connected to the copper ball and its shield is connected to ground at the pipe bottom. The central conductor runs through a Pearson current probe and is then connected to ground. The Pearson probe (mod. 110A, 20 MHz, 0.1 V/A) is located inside a grounded steel box and connected to a digital storage scope by a shielded cable, grounded at both ends.

The idea is to measure the current from the strike target to ground in order to understand when it has been hit by a discharge. By having the current on one DSO channel and the capacitor charging voltage on another channel it is simple to state after how many bangs the target has been hit. To disregard current due to noise, streamers and leaders, and concentrate only on the so-called final jump, a hit is considered such only if the current peak measured is 3 A or higher.

Several trials have indicated that 20 seconds between two bang sequences is sufficient to ensure statistical independence. On the other end, it has been easy to notice measurement correlation for a delay of 5 - 10 seconds. For each operational point, the number of target misses and the number of aluminum pipe strikes have been collected. The probability to hit the target has been calculated as:

Hit % = target_hit_n / (target_hit_n + pipe_hit_n + miss_n) * 100