How can I prevent mold from growing on the surface of my sauerkraut brine?
Brining vs. Dry-Salting
Vegetable fermentation is normally done by one of two methods:

brining (submerging whole or chopped vegetables in brine)
dry salting (mixing chopped vegetables with salt and letting osmotic magic draw fluid from the vegetables to create a brine)

I'm pretty sure you're describing a brining process. Kraut is normally a dry salted application. Sandor Katz's &quot;The Art of Fermentation&quot; is a bible for this sort of thing. See Chapter 5 for a discussion of this; he lists kraut and kimchi as the classic examples of dry salting. You might want to try a more traditional dry-salting process. Katz's Wild Fermentation site has a weight-based dry-salting recipe.
Having said that—it won't guarantee you get no mold.
The Futility of Preventing Mold
I get that you're asking how to prevent mold, but the real question is: Can you absolutely, 100% of the time, prevent mold?
Maybe you could with with an industrial-grade setup, but I'm not even sure of that. I've been making kraut and many other vegetable ferments for almost a decade now, and I can tell you this: Sometimes mold happens. It doesn't have to happen often (I see it very rarely), but if it does? That doesn't mean you did something wrong.
From The Art of Fermentation section &quot;Surface Molds and Yeasts&quot; (p. 103 in my hard-cover printing):
&quot;An inevitable aspect of [fermentation] technique is the edge, where (in an open vessel) the surface of the liquid... comes into contact with oxygen-rich air. The meeting... encourages rich biodiversity, where molds and yeasts frequently develop. Surface growth is common and normal; it should be removed, bit is not cause for alarm and it does not ruin your fermenting vegetables.&quot;
Minimizing Mold
Having said that—I'm with you. Mold grosses me out. I try to prevent it, and usually I can.
In my experience, the wider the vessel's neck, the more mold and kahm (yeast) develop. I have good results with 2-quart mason jars, which have a low neck-to-volume ratio. That minimizes the &quot;edge&quot; that Katz describes. For large batches, that means multiple 2-quart jars, but the control is worth it to me.
I also check the surface of my ferments every 2-3 days and skim off any developing kahm or mold. Every time I check, I'm exposing the surface to more mold and yeast spores... but if I catch it when it's the size of a pinhead, it won't grow to the size of a quarter.
I've also had much better success since I started using actual fermentation weights and vented lids for my mason jars. Any will probably do, but I've been using this weight and this lid.