Screen Grid resistors are used for a number of reasons, be it:
1. To eliminate garden variety (non-destructive) parasitic oscillations with tubes prone to such behavior,
2. To limit screen grid dissipation under conditions of high power output, and
3. To prevent output tube arcing in circuit/tube combinations prone to producing such behavior.
If the resistors are part of the original design and used/required only to address issues relating to #1 above, they are correctly called a "stopper" resistor, since the formation of parasitic oscillations is what they are stopping from happening. These resistors will typically be of a .5 watt rating, but can rated as high as 1 watt, with values as high as 470Ω depending on the tube they are serving.
Screen Grid resistors included in the original design to address the issues of #2 above will find values as high as 2.2K, with wattage ratings of 2 or even 5 watts not being uncommon. Values and ratings this high are almost exclusively reserved for high power true pentode tubes types like the EL34, where the screen grid is not aligned with the other grids in the tube, which allows screen grid current to soar under conditions of high power output and/or overload. In this case then, the resistors act to limit screen grid dissipation to protect the grid under those conditions, and therefore the tube as a whole. Resistors of this type can also act to address issues relating to #1 above as well. For applications like large sound distribution and guitar (production) amplifiers, oversized resistors were often used to favor ease of servicing. Back in the day when tubes were inexpensive and readily available, it was far easier and more economical to simply replace a tube than open a unit up to replace a screen grid resistor. Using a robust rated resistor then ensure that during a catastrophic event, it was the tube that burned up, and not the resistor. These types of resistors are often (and mistakenly) called stopper resistors as well, but are more correctly called screen dropping resistors.
Addressing item #3 above involves adding a screen grid resistor to a design where one was never originally included. Because they are added specifically to prevent any tendency towards output tube arcing, I coined the term "Screen Stability" resistor to identify their purpose, and the fact that they are not part of the original design.
Some designs certainly should have originally included them but didn't, with their resulting reputation of unexplained output tube arcing being near legendary. The Eico HF-89 is one such example. More common however, is the unit that was never particularly prone toward output tube arcing, but began arcing after the unit was recapped.
Many years ago now, I determined that such events were always a screen grid related event, with this element invariably arcing to either the cathode or control grid. The arcing began when modern (read that as: Low ESR) electrolytic caps were used to replace the original specification capacitors in the power supplies of favorite amplifier designs. The low ESR value of these caps, in conjunction with the screen grid itself, allowed a potent tank circuit to be created, that could be triggered to destructive levels anytime an errant transient came along to do so. Simply setting the needle down on a record was often all it took. An amplifier that was equally famous for output tube arcing after it had been restored was the Dynaco MK III. Adding Screen Stability resistors then to either the Eico or Dynaco amplifiers (and others like them) eliminates the tendency towards arcing.
Unless an amplifier is grossly abused (full or overload power developed with no load connected), virtually all arc events will occur at the screen grid of a tube. A plate arc can generally only occur when the back EMF from the collapsing field of an unloaded output transformer rares back from a full power signal applied to it. With no place for the energy to go, the plate receives a sucker punch of many thousands of volts in this scenario, giving way to an arc at the plate. In high fidelity applications however, this rarely if ever occurs other than by accident.
When adding Screen Stability resistors, the smallest practical wattage size is recommended so that the resistor will also tend to act as a fusing agent as well. A rating of .25 watt generally works just fine for amplifiers up to and including a power output rating of 35 watts when that power is developed from two output tubes. A .5 watt rating is usually sufficient for power levels above 35 watts developed from two tubes. Metal film resistors are highly recommended in this application, since they tend to open most quickly in case an arc event does occur. For the purposes of acting to prevent screen grid arcs, a value of 100Ω works well for virtually any tube type. Finally, and rather obviously, any resistance added to the screen grid circuit in an original design to address issues relating to #1 and #2 above, will also suffice to address #3 as well.
Dave
