It looks like powdery mildew. Here's a website I found with similar pictures and some info:
"Podosphaera macularis (formerly Sphaerotheca macularis), a fungus. Powdery mildew is occasionally a serious disease on foliage, new canes, and fruit of red raspberry in the Pacific Northwest. It also can infect 'Loganberry' leaves. The fungus overwinters as mycelium in dormant buds of stunted cane tips or as chasmothecia. Optimum conditions for spore germination and infection are 65°F to 80°F with relative humidity of 97% to 99%. In May, leaves develop lesions that produce fungal spores that are blown to healthy foliage. In June small, secondary-infection lesions appear on vegetative tissue and developing fruit."
This one gives organic treatments:
The first option given is spraying with a 10% milk solution. I wonder how that works. It also says the fungal organisms may develop a resistance, so to use it intermittently.
I would probably remove the branch.