Most of you wrote that your antennas work below the voltage necessary to
start the electron emission.

But in reality the emission take place at all voltages.

" Attempts to understand autoelectronic emission included plotting
experimental current-voltage (i - V) data in different ways, to look for a
straight-line relationship. Current increased with voltage more rapidly than
linearly, but plots of type (log(i) vs. V) were not straight"

"A breakthrough came when Lauritsen[13] (and Oppenheimer independently[14])
found that plots of type (log(i) vs. 1/V) yielded good straight lines. This
result, published by Millikan and Lauritsen[13] in early 1928, was known to
Fowler and Nordheim.
Oppenheimer had predicted[14] that the field-induced tunneling of electrons
from atoms (the effect now called field ionization) would have this i(V)
dependence, had found this dependence in the published experimental field
emission results of Millikan and Eyring,[10] and proposed that CFE was due
to field-induced tunneling of electrons from atomic-like orbitals in surface
metal atoms. From: http://en.wikipedia.org/wiki/Field_electron_emission

Electrons escape from each charged body. Your antennas emit electrons and
for this reason they need the sink of electrons (the earth/chassis/
counterpoise).

Best Regards,

S*