Just how creative should the DM let the Artificer be? One of my players is a guy who thinks way too hard on how to solve problems he's not meant to 'Solve' as a player.

For example, I have a little set-piece in place for my campaign setting where there are roaming clouds of illusion magic that will appear at random times around the region. These clouds effectively have the magical power of 9th-level illusion magic violently swirling within them, causing all kinds of chaos when they appear.

They are meant to be a hazard that the players are meant to avoid, but my Artificer player thinks differently. He surmises that with all his tool proficiencies like Smith's tools, Tinker's tools, Alchemy supplies, etc., that he should be able to build any kind of contraption he wants given time. I tried to explain that doing so would grind the game to a halt, as he would need to study for years in game time to come close to building the 'giant magical vacuum' that can suck up the illusion storms, and he wouldn't even be able to determine whether it would work or not.

This is only one of many hypothetical arguements we've had in the past, and I would just like a reference to point to in the future if he ever picks to play Artificer again:

Exactly how much of the hypothetical creativity should be allowed to actually happen when a player uses meta knowledge to build machines in a D&D setting? What power do artisan's tools actually have in the hands of an Artificer?

Artisan Tools function more-or-less the same for Artificers as they do for other classes; with a few perks

Any character with proficiency in Artisan's Tools is able to use those tools to craft items, magical or non-magical.

The non-magical rules are introduced in the Players's Handbook, expanded upon to include magical items in the Dungeon Master's Guide, and then revised/rebalanced in Xanathar's Guide to Everything.

You can craft nonmagical objects, including adventuring equipment and works of art. You must be proficient with tools related to the object you are trying to create (typically artisan's tools). You might also need access to special materials or locations necessary to create it. For example, someone proficient with smith's tools needs a forge in order to craft a sword or suit of armor.

For every day of downtime you spend crafting, you can craft one or more items with a total market value not exceeding 5 gp, and you must expend raw materials worth half the total market value. If something you want to craft has a market value greater than 5 gp, you make progress every day in 5-gp increments until you reach the market value of the item. For example, a suit of plate armor (market value 1,500 gp) takes 300 days to craft by yourself.

—Crafting, Player's Handbook, pg. 187

Magic items are the DM's purview, so you decide how they fall into the party's possession. As an option, you can allow player characters to craft magic items.

The creation of a magic item is a lengthy, expensive task. To start, a character must have a formula that describes the construction of the item. The character must also be a spellcaster with spell slots and must be able to cast any spells that the item can produce.

Moreover, the character must meet a level minimum determined by the item's rarity, as shown in the Crafting Magic Items table. For example, a 3rd-level character could create a wand of magic missiles (an uncommon item), as long as the character has spell slots and can cast magic missile. That same character could make a +1 weapon (another uncommon item), no particular spell required.

—Crafting a Magic Item, Dungeon Master's Guide, pg. 128

Emphasis mine, the relevancy of which should become quite apparent.

Artificers have two particular perks as they relate to these rules: the first is that they have a special feature, the details of which are decided upon by their subclass, that enables more efficient crafting than other characters:

Crafting. If you craft a magic item in the [potion/scroll/wand/armor] category, it takes you a quarter of the normal time, and it costs you half as much of the usual gold.

—Tools of the Trade [Alchemist/Archivist/Artillerist/Battlesmith], Unearthed Arcana: the Artificer Returns, 2019-05-14

The other major perk is their ability to at sunrise "infuse" items so that they behave as though they were magic items, but for our purposes we don't need to think about that perk.

The important part is, while their ability to do so is greatly improved over that of other classes, Artificers aren't strictly capable of making better or more powerful magic items than anyone else: they just have an inherent affinity for doing so.

So about their plans to subjugate 9th level Spell Effects...

As DM, there's good reasons to at least encourage the Artificer in question to try to tackle this. It might lead the campaign in an interesting direction, or create new ways for you, the DM, to interact with the narrative of your story.

But, naturally, there needs to be limitations. And there are some very good hints to help us work out how stringent those limitations might have to be.

If the clouds are "Level Nine Spells", an object capable of subjugating them probably also needs to produce a "Ninth Level Effect"

This seems perfectly reasonable, yes? I'd like to think the player trying to do this will respect this as well.

There's also precedent for this: the spell Imprisonment specifically says "A dispel magic spell can end the spell only if it is cast as a 9th-level spell, targeting either the prison or the special component used to create it." (PHB, pg. 252), so it's not unreasonable to rule that other ongoing effects of "Ninth Level Power" might have similar restrictions.

So what is required for a player to create an item that can produce a "Ninth Level Effect"? Well, there's two rules we'll want to look at: the restrictions on crafting magic items of various rarities, and the rules for creating whole new magic items to place in a campaign.

Power Level. If you make an item that lets a character kill whatever he or she hits with it, that item will likely unbalance your game. On the other hand, an item whose benefit rarely comes into play isn't much of a reward and probably not worth doling out as one.

Use the Magic Item Power by Rarity table as a guide to help you determine how powerful an item should be, based on its rarity.
beginarrayl
hline
textMagic Item Power by Rarity \ hline
textRarity & textMax Spell Level & textMax Bonus \ hline
textCommon & text1st & — \ hline
textUncommon & text3rd & +1 \ hline
textRare & text6th & +2 \ hline
textVery rare & text8th & +3 \ hline
textLegendary & text9th & +4 \ hline
endarray

—Creating a New Magic Item, Dungeon Master's Guide, pg. 284

Moreover, the character must meet a level minimum determined by the item's rarity, as shown in the Crafting Magic Items table. For example, a 3rd-level character could create a wand of magic missiles (an uncommon item), as long as the character has spell slots and can cast magic missile. That same character could make a +1 weapon (another uncommon item), no particular spell required.

[...]
beginarrayl
hline
textCrafting Magic Items \ hline
textItem Rarity & textCreation Cost & textMinimum Level \ hline
textCommon & text100 gp & text3rd \ hline
textUncommon & text500 gp & text3rd \ hline
textRare & text5,000 gp & text6th \ hline
textVery rare & text50,000 gp & text11th \ hline
textLegendary & text500,000 gp & text17th \ hline
endarray

—Crafting a Magic Item, Dungeon Master's Guide, pg. 128

So these two tables in conjunction with each other tell us some very important information:

• A Magic Item or Device that can produce a 9th level spell (or a "Ninth Level Effect") probably qualifies as a Legendary rarity item.


• A character who wishes to create a Legendary rarity item is required to be 17th level, and spend materials equivalent to 500,000gp (Disclaimer: Xanathar's Guide to Everything lowers the gold cost substantially, and as DM, I generally prefer those rules to the DMG rules; Your Milage May Vary)
  

So in total, this Artificer (or any character for that matter) is probably going to be required to be at least level 17 before they can successfully create the kind of "Magic Cloud Vacuum" they intend to create. You might tweak these rules for your own purposes (maybe Artificers get access to higher level item recipes at a lower level? Maybe the clouds are more like sixth or seventh level instead of ninth?) but at least by the standards set by the game itself, it's certainly outside the capabilities of a low level character.

Sidebar: per the way the rules are written, if such a character wanted to produce an item that actually produced a Ninth Level spell, not just a "Ninth Level Effect", they'd need to be able to both cast the spell and consume a Ninth Level Spell Slot—which Artificers never get. Personally, I would handwave that for Artificers, since it feels thematically inappropriate for a Wizard to be more capable at producing Magical Items than an Artificer, but in general it is a good rule to follow.

Conclusion

Personally speaking, as DM, I prefer to be as permissive as possible when it comes to player decisions, unless it's obvious that they're abusing the rules and in doing so making the game unfun for everyone else. It's not obvious that that's what your player is doing—from your description it just sounds like they're really enthusiastic about the possibilities of a character that can create magic items—so I think it's okay to help them reach a point where they might be able to do something like this. But you need to make it clear that that's not going to happen for a new character.

Like illustrated above, there's a set of relatively reliable rules that tell us that what they're trying to do is theoretically plausible, but they should be required to at least fulfill the minimum requirements. And if you use these rules as-is, that means they need to reach level 17.

So if your campaign runs for long enough that they get to or near level 17, you should go ahead and set them up for their quest to build the magical Cloud Vacuum that will let them do exactly that. Just make sure it's clear to them that that's a long-term goal, not something they should expect to be able to do as a new or even moderately veteran character.

A player is handing you a campaign-spanning objective loaded with adventure seeds

This seems like more of an opportunity than a problem.

The player needs to:

1. Find out what the clouds actually are


2. Why they are there


3. How they can be stopped


4. Gather the required materials


5. Overcome the people who don’t want home to succeed because reasons


6. Succeed


7. Find out the unintended consequences of succeeding


8. Deal with those

There are a good two dozen adventures in that!

Of course, this can be a secondary story with clues scattered through the main thrust of your campaign. Or even one or a few side adventures so that everywhere he goes everyone wants to met the guy who beat the clouds.

This is not the character for this game.

I'm going to assume that you had a session zero and that everyone is on the same page that they're Adventurers (heroic sound effects).

Depending on level, the character may or may not even have the magical ability to do some of the things he wants, but there's a more important issue: Time.

The artificer, with enough time, money, and know-how, very likely can MacGyver all sorts of zany solutions, with DM-approval. However, the group is playing Dungeons and Dragons (more heroic sound effects), not the My Little Band of Tinkerers minigame.

The Artificer in question, I'll call him Arthur, does not have enough of the resource of "playing this game with the rest of us" to spend on creating some massive magical spell vacuum. Your explanation is correct.

There are a few ways to deal with this

You said it: it would take in-game years. The character leaves the party to follow his research and the player of Arthur and roll up a new character to go adventuring with the party.

Sit down with player of Arthur and re-explain the session zero goals, and how (unfortunately) this character doesn't jive great with those goals. There's no issue with him spinning up a different character at the same level with equivalent (or the same) gear. Or he can use the same character with a different mindset. I assume, you still want this person to play in the game, so work with them.

IF you did not have a session zero, or there are other synergy problems with the game, this is a great time to have one. Allow everyone to make sure their on the same page. What kind of theme are we running? How long should an adventuring day be? Is everyone assumed to be good? etc.

I'll start by listing three "facts":

1. A DM's word is final




2. There is nothing wrong with players having goals and showing creativity



3. 
   

   The game is meant to be fun for all

   
   
   

   The question is how to successfully combine these three facts.

   
   

First, you many want to point out that artisan tools, smith's tools and so on are not magical and can do nothing on their own. In the hands of an artificer they function as spell focii, but that still doesn't mean they do anything more than an ordinary set of tools other than enable the artificer's spell-casting (mechanically speaking).

Second, if the player insists that he doesn't want his character to do anything other than sit in his house and research and build, and willfully ignores all plot hooks, then there may not be much you can do other than encourage the player to play a different character that is willing to adventure!

But as long as there is room for compromise, then there is nothing wrong with stating that the character simply doesn't have the knowledge yet but, assuming he does go an adventure (however reluctantly), planting a few little tidbits of lore here and there permit progress towards his goal without stalling your campaign.

For example: the players come across some lore hinting at the origin of these mysterious storms. This leads into adventures where they discover a wizard, or the stories of a wizard, or tracks evidence of a wizard, who previously tried to stop them but disappeared in the Bad Lands.

This in turn leads to more adventures where they discover the wizard's research and find out that there may be a way to build a machine to stop the storms, but it requires a very specific ritual and some very specific spell components.

This leads on to... more adventure, and ultimately a success or failure of this goal.

With a bit of imagination and planning, you could merge these 'side-quests' and the player's desire to build a machine to stop the storms into your campaign.