Re: More on spark delay

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Bert Hickman by way of Terry Fritz <twftesla-at-qwest-dot-net>" <bert.hickman-at-aquila-dot-net>

Hi Ken,

Sorry for the delay in responding. I actually meant to respond the first
time you proposed it, but didn't have the time at the time.. :^) 
Comments are interspersed below...

Tesla list wrote:
> 
> Original poster: "by way of Terry Fritz <twftesla-at-qwest-dot-net>"
<Kchdlh-at-aol-dot-com>
> 
> I've put forth my hypothesis more than once that the relatively high
> rate-of-rise of spark-gap-coil voltage is the reason that spark-gap
sparks are
> longer than SSTC sparks.  I've proposed that that high rate allows the toroid
> voltage to rise higher during the time it takes for the spark to propagate.
> That time period exists due to the necessity to heat and displace the air
along
> the spark's path.

You are correct, but perhaps for different reasons. Once initiated,
leader growth proceeds in discontinuous steps. Each leader jump is
accompanied by a very rapid transfer of charge from the topload though
the leader root and out the far end streamer tips. These charge
transfers are brief (10's-100's of nanoseconds), and each one results in
a corresponding drop in topload voltage. Further leader propagation then
STOPS until the terminal voltage can recover to an even greater
potential (to overcome increasing resistance of the leader as it cools
down). If the terminal voltage can't be replenished quickly enough, the
outer ("thinner") portions of the leader cool down, and the following
leader must do more work reheating the previous path, leaving less
energy available to further extend total leader length. 

> 
> The notion has received scant attention.  I may be repeating myself but
here's
> an observation I just made today:   In my SSTC, the toroid voltage's rise &
> fall is extremely stable from spark to spark.  So, I can sync the scope to it
> and accurately gauge the rise and fall.  I find, at commencement of the
spark,
> that the toroid voltage falls abruptly, at first, to about 70% of the level
> that it holds during the remaining 5 milliseconds of the spark's duration.

Once initial breakout is achieved, you've apparently reach an energy
balance between I2R losses in the leader (due to displacement current
flowing to leader and streamers capacitance) and energy replenishment
via the driver and resonator. Since the system can't "overpower" the
losses, the terminal voltage can't increase, and further leader
propagation ceases.

> That fall seems to take place well within 1 cycle of the excitation, which is
> at ~140 KHz , and it always occurs at a negative half-cycle (indicating to me
> that the spark initiates when the toroid is 'crowded" with electrons and not
> otherwise).  It then takes just about 100 microseconds longer for the voltage
> to decline further to the steady level.

The terminal voltage behavior is consistent with rapid charge transfer
during streamer and leader formation during initial breakout. However,
the terminal's polarity is somewhat surprising, since leaders seem to be
preferentially initiated when the topload is positive (i.e., for
"cathode directed" streamers) than when negative. 

> 
> Clearly, at the instant of the 30% drop, the impedance of the initial
spark has
> appeared in parallel with the impedance of the capacitance between the toroid
> and ground.  But at the end of that instant, the spark impedance is still
> relatively high since its presence in the series circuit of
> ground/secondary/toroid:ground capacitance/ground (across "toroid:ground
> capacitance") has diminished the toroid voltage by only that 30%.  The spark
> impedance then relatively-slowly decreases during the following 100 us,
causing
> the toroid voltage to correspondingly diminish.

Agree. But any significant decrease in terminal voltage will tend to
choke off any further leader propagation. Joule heating (from
displacement current flow through the resistive leader) is sufficient to
keep the leader hot, thereby keeping the effective loading relatively
constant.  

> 
> So my supposition remains:  It is the capability of spark-gap systems to
> deliver higher power during the (at least first part of) 100 us or so that
> allows for the longer sparks.  And it is the physical/thermal inertia of the
> air in the path of the spark that causes the 100-us phenomenon to exist.
> 
> But perhaps this is old-hat to spark experts.  Comments?...
> 
> Ken Herrick

I suspect the underlying reasons are likely a bit more complex. Let's
assume that initial breakout occurs at some point below the peak output
voltage of the system. Due to the larger pulsed power and faster
primary-secondary energy transfer rate, a disruptive coil can more
easily "overpower" the additional capacitive loading and Joule heating
losses added by a newly formed leader and streamers. If the system can
transfer sufficient energy to restore, and further increase, topload
voltage during the remainder of ring-up, the existing leader may further
extend itself in another "jump". However, each leader extension is still
a stepwise jump, and each extension if accompanied by a downward delta
of topload voltage, followed by voltage recovery (assuming secondary
ringup is still underway). With sufficient bang size and high coupling,
the leader extension-recovery sequence can occur multiple times even
during a SINGLE bang, leading to longer leaders even for single shot
mode of operation. Under these conditions, an observer would see longer
"single shot" lengths - this may be what is occurring during pulsed mode
VTTC and SSTC operation when the rep rate is significantly below 100
BPS.      

At bang rates of about 100 BPS or above in still air, the air's
dielectric strength doesn't fully recover between bangs, terminal
breakout voltage is now lowered, and the leader tends to follow at least
the same root path blazed by its predecessor. Since the next leader
requires less energy to re-form, more energy is available to further
extend overall leader length, and accounting for observed leader growth
from bang-to-bang. If repetition rates are kept significantly below 100
BPS, each leader forms pretty much as an independent event, and average
leader length is considerably shorter. 

In your system, the low rep rate (16 BPS) prevents any bang-to-bang
leader extensions. And once a leader is initiated, the system cannot
deliver energy to the topload quickly enough to overcome the additional
joule heat losses and additional capacitance of the leader/streamers.
Once a leader is launched, charge is rapidly transferred out of the
topload and topload voltage suddenly declines (~30%). Leader formation
and propagation typically occurs in hundreds of nanoseconds or less. The
abrupt reduction in terminal voltage stops any further leader
propagation in its tracks. 

In addition, your system has a comparatively low rate of energy
replenishment (requiring 32 cycles at Fr). So, once breakout occurs, the
initial reserve of the secondary's reactive energy (analogous to a
secondary "bang size"?) is depleted more quickly than it can be
restored. The resulting net energy loss causes the terminal voltage to
further decline (~14 cycles of Fr) until an eventual energy balance is
reached between incoming driver power and outgoing leader/streamer
losses (remaining ~5 msec). Because there's no further leader
propagation after the initial one, any subsequent energy transfer goes
into displacement current into/out of the leader root, keeping the
existing leader hot, fat, and bushy... but short. 

Hope this helped a bit...

Best regards,

-- Bert --
-- 
Bert Hickman
Stoneridge Engineering
Coins Shrunk Electromagnetically!
http://www.teslamania-dot-com