Tube Vacuum vs Cathode Area, Do We Need Filament Warmup?

[steve]

I was contemplating the number of gas atoms inside a typical vacuum tube vs
the number of electron emitting atoms on the surface of an oxide Cathode of a
KT88. 

As one can see quoted below, the difference between oxide atoms vs gaseous atoms is
quite stark. So I have to question how can a cold cathode be seriously damaged by so
few positive ions with such low energy levels? Some info.

"Outer space is an even higher-quality vacuum than the best laboratory vacuum tubes — in
intergalactic space, there are fewer than one hydrogen atom per cubic meter,

compared to about 100 particles per cubic centimeter in ultra‑high vacuum chambers.
Particle density comparison."

In a properly evacuated, high vacuum tube KT88, an exaggerated number of ions is 5000 atoms, 5 x 10 to 3 atoms —
not a significant number of gas molecules to ionize.

A vacuum tube is designed to be a hard vacuum, meaning the internal pressure is extremely low —
"typically on the order of 10−6 to 10−9 torr. At these pressures, the number density of gas molecules is
so small that the probability of ionization is negligible under normal operating conditions."

"Estimated Number of Atoms on the KT88 Oxide Cathode Surface? A reasonable order of 10¹⁸–10¹⁹ atoms.

Notes

This is a surface atom count, not the total number of atoms in the entire cathode structure

"Speed of Positive Ions to the Cathode in a Vacuum Tube

"In a vacuum tube, positive ions can travel to the cathode at speeds on the order of tens of
thousands of meters per second — roughly 10⁴–10⁵ m/s — under typical operating voltages."

So 10 to the 18th oxides atoms (1 x 1000000000000000000) vs exaggerated 5000 ions in a hard vacuum.
Suppose we multiply the number of ions by 1000 times to 50,000 ions created.

I used two different Ai for their response.

Me: "suppose we have 10 to 18th atoms on cathode of KT88. Would 50000 ions shorten life of the
tube starting with cold cathode ?"

Grok: "No. 50,000 ions is negligible and would not meaningfully shorten the life of a KT88 (or similar
oxide-cathode power tube), even starting from a cold cathode.

Why the number of atoms matters.
A typical oxide cathode (Ba/Sr/Ca oxides on a nickel sleeve, as used in the KT88) has a coating with a
macroscopic thickness corresponding to hundreds of atomic layers or more. Literature values for
oxide coatings put the lower limit around ~400 atom layers and practical coating weights on the order
of several mg/cm².

Even a conservative estimate of the active surface or near-surface atoms is in the
range of ~10¹⁵ atoms/cm² for a monolayer, scaling up rapidly for the actual coating volume. Your
figure of ~10¹⁸ atoms is therefore a plausible order-of-magnitude total for the relevant emitting material
on a power-tube cathode of this size.
50,000 ions is ~5 × 10⁻¹⁴ of that quantity. Even if every ion removed multiple atoms, the fractional loss is
vanishingly small."

A high vacuum 5000 ions would create vastly less destruction to a cold cathode than the above example.

From Copilot Search:

"Effect of 5,000 Ions on KT88 Cathode Life

A single pulse of ~5,000 ions striking the KT88's cathode is extremely unlikely to shorten its service life,
especially if the tube is new and the ions are not accompanied by high-energy bombardment or arcing.
Why the ion count is negligible

Ion energy:
In a typical vacuum tube, ions in the cathode region are low‑energy (a few eV) unless there is a strong
electric field or discharge. Even at 5,000 ions, the total energy deposited is minuscule compared to the
thermal and electron‑emission loads the cathode already endures.

Comparison to normal operation:
A KT88 in normal audio operation emits tens to hundreds of milliamps of electron current — that's 10¹⁸–10²⁰
electrons per second. A 5,000‑ion pulse is many orders of magnitude smaller in total charge than the continuous
electron flow during normal use.

I do wonder about nickel cathode sleeve impurities though.

So I have to wonder if a tube's life is affected by ion bombardment. 

Other thoughts are welcome.

Cheers

steve

[steve]

Major change in first post as I delved deeper into the subject of ion
bombardment.

Cheers

steve