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I need people to get zapped more often in my world.
Zapping others with electricity must be a more viable option than it is in our world.
Shooting cables at people to zap them? Nah....I prefer the wireless version.
What needs to change in Earth's atmosphere to make air more electrically conductive?
Replace nitrogen with another inert gas.
The two most obvious candidates, argon and neon, are actually slightly harder to ionize than nitrogen (their first ionization energy level is higher), but they have a significantly lower dielectric strength which means they break down in a much weaker electric field than air normally does.
The wikipedia page on dielectric gasses is mostly interested in things that don't break down as easily as air, but it does list the relevant values... argon breaks down in 1/5th the field strength of air, and neon in one fiftieth. A separate source, Dielectric Strength of Insulating Materials gives figures of more like .18 for argon (slightly lower) and .16-.25 to neon (much higher than wikipedia).
In any case, both gases are easier to ionize with a lower voltage spark, and once ionization has started then avalanche breakdown can proceed providing plenty of ions to carry electrical current and generate a nice big spark. In the case of neon, that spark will be a lovely red color, though argon will have a bluey-purple color just like nitrogen and air. Remember that lowering the dielectric strength of the atmosphere is going to have all sorts of interesting knock-on effects with weather (lightning will be more common, though perhaps not as strong) and electric equipment which will be much more prone to arcing... a potentially serious problem for power grids.
In terms of planetary atmosphere development, neon has greater cosmic abundance but being a very light gas it is more likely to be lost through atmospheric escape unless the surface gravity of the world was much higher. For anything but hard scifi though, you can quietly ignore that issue.
Shooting cables at people to zap them? Nah....I prefer the wireless version.
You could just use an electrolaser, you know... use a laser pulse to ionize a couple of trails of air between you and your target, and then run a current through them. You need moderately futuristic technology to make electrolasers compact enough to be useful as human-portable weapons, but they're entirely plausible and don't require replacing an entire planetary atmosphere.
You probably don't want to combine the two, because that will reduce the voltage you can use with your electrolaser channels before the atmosphere between them breaks down and shorts the circuit before it reaches the target.
edit It has been pointed out that removing all the nitrogen from your atmosphere may have some other unwanted side effects (like stopping the nitrogen cycle, and ending all life in a relatively short timescale), so caveat emptor and all that. If you wanted to go for an argon atmosphere, consider also having a read of this answer I gave to the question, "Could a hypothetical planet composed of a neon-oxygen or argon-oxygen atmosphere with Earth-like pressure levels sustain life?" which briefly mentions some of these issues.
Salt fog.
At sea or on the coast, sea spray carries droplets of salt water into the air. When these droplets dry up the salt particles they carry can remain airborne and travel distances. In foggy conditions, water vapor can nucleate around a salt particle, producing salt fog at some distance from the sea. Because salt water facilitates ion movements, salt fog accelerates corrosion. Salt fog also improves the conductivity of air.
The lightning striking probability for offshore wind turbine blade with salt fog contamination
The blades of an offshore wind turbine are prone to be adhered with salt fog after long-time exposure in the marine-atmosphere environment, and salt fog reduces the efficiency of the lightning protection system. In order to study the influence of salt fog on lightning striking probability (LSP), the lightning discharge process model for the wind turbine blade is adopted in this paper considering the accumulation mechanism of surface charges around the salt fog area... The simulation results indicate that the receptor and conductor area close to the receptor area are more likely to get struck by lightning, and the LSP increases under the influence of salt fog. The validity of the model is verified by experiments. Furthermore, the receptor can protect the blade from lightning strikes effectively when the lateral distance between the rod electrode and receptor is short. The influence of salt fog on LSP is more obvious if salt fog is close to the receptor or if the scope of salt fog area increases.
Your world has perpetual salt fog. Lightning strikes and other sorts of shocks are frequent. The people of your world are called the Salt Fogs and they are all pirates except one. When the Salt Fogs get shocked they go "Arrrr.. that shock shivered me main mast!".
Or something like that; not the same thing every time, but similar.
Also the Salt Fog pirate dogs bark in a characteristic way when they get shocked.
Let the air be mildly radioactive, and that makes it much more conductive - but if radioactivity and ionization are below a certain threshold, the air is still brethable.
Long term effects might be a worry though.
(This is how the very first "radiation detectors" worked - by charging an electroscope's foil arms inside a jar of clean, dry air. The electroscope's arms would visibly repel each other, until their charge dissipated; which would happen at different speeds depending on the air's ionization).
Zapping may refer to the discharge of static electricity (e.g. you wear rubber, tanked shoes and walk on a synthetic wool carpet. You then touch a grounded water tap. YEOW!). For this kind of zapping you want the air to not dissipate your charge, so no radioactivity, dry air, and the appropriate materials around (wool, synthetics).
Or you want people to be more taserable. This can be done technologically. Usually, tasers work by shooting thin conducting wires charged with a high voltage. But there's research on using ultraviolet laser pulses to "drill" ionized tunnels through the air, with conductivity high enough than a discharge would run through the twin tunnels rather than shorting them out. For this, too, you need dry air (the tunnels must remain isolated) and then it's just a matter of developing the appropriate emitter. You might even have some handwaved "dust particle emitter" that shoots laser-driven conducting particles towards the target, building a pair of ion-and-dust virtual-wire channels. You still have the problem of the last millimeter (which taser avoid by ending the wires with two sharp needles): the ionized tunnel ends on the target's clothes, which might be thick and insulating.
Then finally the spontaneous breaking charge in the atmosphere (i.e. lightning bolts). For that you want conducting air, so ionization, therefore ionizing radiation from some source. Ordinary air breaks at about 30.000 V per meter (you need 300.000 volts to cover ten meters of dry air). Ionizing radiation may decrease that down to about 1500 V/m . Remember that the electric discharge will still try to reach the nearest ground, which might not be the target.
For example: in spontaneous conditions, a discharge from 2 m height will hit a man's head at 1.5 meters if he's grounded, because 1.5 meters is a shorter path than 2 meters. No amount of ionization will allow the discharge to hit the man if he's at 3 meters: the discharge will rather hit the ground, which at 2 m distance will be nearer.
Drilling a UV-laser tunnel from the point source to the man will make resistance lower only on that path. You still will not be able to use more than 60.000 V (because at 30.000 V/m, breakage in normal air will occur at 2 meters). So to hit the man at 15 meters, the UV pulse has to decrease breakage threshold to 60.000/15 = 4000 V/m or lower. And, doing the calculation in reverse, a threshold of 4 kV/m will allow hitting at no more than 15 m range if shooting from a height of 2 meters. Shooting from the hip (at 1 m from the ground) will have a proportionately shorter range.
