Is there a way to log the current in SMU mode when sourcing voltage and measuring current?

Not using that software tool. To log DC measurements to a file over time you need to use the Data Logger tool which include a set of controls like the ones in the more simple Meter Source tool. For capturing AC measurements data Traces (Curves) from the Time sweep screen in the main ALICE desktop should be used, File->Save To CSV.

Sorry but that program (the Data-logger) only stores voltage readings to the log file. Also the log file is only closed when the program is exited. I will look into changing this in the next release. For right now use the Main ALICE desktop program to save current data samples to a file.

What I want to do is source a voltage, then measure and log the current.  I can use the Data-logger program to source a voltage and measure current,  but just can't save the current data.

When do you think you can release the new Data-logger program so it can log the current?  I want to log data for a long time, a least a week, with a low sample rate.  Is that possible?

If one of the provided programs does not meet your requirements we generally recommend  users write their own custom applications. Matlab and the data acquisition tool box from the Mathworks is a popular tool.

Do you have any skills at writing Python programs? If you do you can customize the source code of one or the other of the examples or full programs on the Analog Devices GitHub repositories here:

https://github.com/analogdevicesinc/libsmu/tree/master/bindings/python/examples

Or here:

https://github.com/analogdevicesinc/alice/tree/Version-1.3