Unfortunately there's not currently a way to automate a percentage up front. You can choose 'pay before processing' as your checkout flow (in financial settings) which will require them to pay if they want to submit an order (it will let them save a bid regardless).
Other than that you can use triggers to remind them to pay, and there's also a trigger that you could use to notify yourself when a payment is made, but that will be for any and all payments, and will not control the 50% requirement.
Also, depending on your customer base, you may find success in educating your repeat customers that their orders won't be verified or started until they pay 50% up front - that would require you to set up some triggers to alert the right people to check on orders and payments.