A staff has nothing to do with mana
A staff, or channeling artifact, is a mage's connection to the hidden energies of the world.
The staff doesn't tap mana, mana is a mental resource that a mage has and regenerates. Mana itslf doesn't kill people, other than maybe the mage itself.
The artifact, instead, is a type of portable power socket. Nearly no one really knows why some are better than others or what makes them trickle, the only thing that is known is that some let you sputter little sparks while others can help you unleash torrential lava
Here's the reasoning:
A Mage is a Hacker: I'll be working off this analogy.
* you have an energy pool that you can use to write code (replenish with caffeine, sleep)
* you learn algorithms through experience and on special occasions, such as reading stackoverflow
* you can throw around exploits, animate machines, calculate secrets
* your creations are more effective and take less energy the more you know about the topic - represented by a stat like intelligence
* your botnet (or size thereof) increases your capacity to crack stuff faster
Theory of Magic
A mage has a certain amount of manas every they wake from a restful sleep. They can also top it off to a certain degree with potions. 227
How much they have every morning depends on their overall physical health. When depleted, they turn into drooling idiots until they sleep again.
Mana required to prepare a particular spell is:
$$m_s = \frac{d_s - (k_s p_s)}{i}$$
where:
* $d_s$ is the difficulty of the spell (intelligence manas)
* $k_s$ is the knowledge the mage has about the spell (intelligence manas)
* $p_s$ is the proportion of how prepared the mage is to cast that spell (is his tool attuned to the spell yet?) (proportion)
* $i$ is the intelligence of the mage (intelligence)
If $m_s$ requires more than a full tank of mana, the mage will have to spend more than a day preparing for it.
However, a prepared spell is not a cast spell.
To cast a spell, a mage needs a powerful artifact. The time it takes to cast a single instance of a spell (in seconds):
$$t_s = \frac{c_s}{r_a} $$
* $c_s$ is the complexity of the spell, this depends on the choice of spell, not necessarily what the spell is supposed to do (in joules). A spell with a low complexity can be found by a mage with a high $i$, but has a considerably higher $d_s$.
* $r_a$ is the amount of resources available to the artifact(in watt).
Conclusion about the Utility of Artifacts and their Social Impact
This means that if you have a twig you ripped off a tree, you might be able to cast a 10 sparks a second with a certain spell.
However, if you have an Artifact of Mass Destruction, you might be able to launch 1e12 sparks per second with the same spell, enough to act as a propulsion system to get you to the next planet.
Merlin's law says the power of newly produced magical artifacts doubles approximately every two years. Considering that the production of new artifacts is severely limited, the obvious effects this has on the increasing divide between rich and poor has many social philosophers concerned about an imminent departure from democracy and a consequent fall of the civilization in general, dubbed the "Singularity" 261