How many horns can be fired from Alicorn Lance during its duration?

Question

I am somewhat confused by the wording of Alicorn Lance as stated in Elminster's Guide to Magic. The text states:

Alicorn Lance
2nd-level evocation
Casting Time: 1 action
Components: V, S, M (a lock of Unicorn mane)
Range: 120 feet
Duration: Concentration, up to 1 minute

A transparent alicorn (unicorn horn) forms about 2 inches from your brow. Starting the turn you cast this spell, for the duration you can use a bonus action during each of your turns to launch the horn at a creature you can see within range. The target must make a Dexterity saving throw, taking 3d6 radiant damage on a failed save. It is also outlined in silver faerie fire on a failed save, causing any attacks against it to be made with advantage until the start of your next turn. On a successful save the target takes half as much radiant damage, but suffers no other effects.
At Higher Levels. When you cast this spell using a spell slot of 3rd level or higher, the amount of radiant damage increases by 1d6 for each slot level above 2nd.

I am confused about the supposed contradiction between "during each of your turns" and "launch the horn".

Does it return between launches? Does it reappear? Does it ever leave your head in the first place?

Can you launch a new horn each round?

Or is it just a single-shot effect that you can use on one bonus action that occurs during the spells duration?

EDIT
I've added the full text: I was initially confused by the wording of when you can use it, but perhaps the additional details may help uncover intent.

In particular, I can understand the comparison to Spiritual Weapon, as it is also a 2nd level spell that does damage on bonus rounds for 1 minute. However Alicorn Horn does significantly more damage per turn (1d8 + SCM vs 3d6 save-for-half), has a range of 120 feet, and applies a (pseudo) status change.

On the other hand, it could be compared to Guiding Bolt, which is a level 1 spell, has the same range, does slightly more damage (4d6) and also applies a (pseudo) status change. However, it is also a ranged spell attack (misses miss) and applies the advantage only to the next attack before the end of your next turn (as opposed to any attacks)

Note that upcasting spiritual weapon takes 2 levels per dice of additional damage; alicorn horn updates 1 level per dice. Effectively, if it can be read as an attack per turn, it turns a 3rd-level slot into 10 bonus-round-usable, slightly powered up, still allowing spells on actions, level 1 guiding bolts!

Answer 1

Spells do what they say they do.

As you've noted in a comment on your answer, in previous editions, it was specified in the spell that you can only fire the horn once. Two of the principle design philosophies in D&D 5^th edition are "There are no hidden rules" and "Spells do what they say they do". If the spell doesn't say that you can only fire it once, then you should be able to fire it more than once.

Answer 2

The intent of the spell is unclear from the text. As you say, if you launch the horn, it's not clear how you would get it back to launch it again (or whether that's even meant to be possible). Also, in past editions this spell has not been reusable.

I recommend that you resolve this by looking at the balance of the spell. This is a second-level spell that lasts one minute and uses bonus actions, so we can compare it to spiritual weapon, which is also a second-level spell that lasts one minute and uses bonus actions. Spiritual weapon is considered one of the better cleric spells -- some have described access to it as "a class feature for the cleric".

Spiritual weapon does 1d8+WIS damage; if you hit a foe 60% of the time then this is probably (1d8+4) * 0.6=5.1 average damage. This spell does 3d6 save-for-half; if they fail the save 60% of the time then this is (3d6 * 0.6+3d6 * 0.2)=8.4 average damage, which is quite a bit more. It also, as you point, out, applies a status effect.

This spell does have the disadvantage that it consumes your action on the turn you cast it. But overall I think it would be unbalanced if we interpret this spell to be reusable.

Perhaps it's better to interpret this spell as single-use, and compare it to guiding bolt, which does 4d6 damage with an attack roll (average 8.4 damage if you hit 60% of the time, the same as alicorn lance) and applies a slightly-worse version of the same status effect.

The alicorn lance spell is arguably a tiny bit better than guiding bolt, because you can cast it before combat and use it on your first turn as a bonus action. But I do think the spells are comparable.