How to set up first differences model?

I am new to R and only know the very basics. Currently I am trying to estimate a model which is very simple, but I have problems thinking about how to set it up. Precisely, I am trying to estimate the following equation:

a(t) - a(t-1) = alpha + beta1 c(t) + beta2 c(t+1)

My data consists of 341 scenarios and each scenario calculates me 10 values for a and 10 values for c, meaning I got "10 ts", which gives me in total 341x2x10 = 6820 data points.
My problem is that I don’t know how to set this up. I brought my data already into tidy format and now I just want to get started, but how?

• Looping approach

  Should I try to estimate this equation for 1 scenario and then try to loop the resulting code over the other scenarios? And if yes, how exactly would I do so? By using the diff() function, storing the result somewhere, looping over the other 340 scenarios, which would give me 341 stored results? How would I then combine these 341 results in the end?

• Time series / panel data approach

  Should I rather focus on "the panel data character" of my data? (to be honest I am not even sure if it’s panel data or time series). In that case I would read a bit more into working with time series / panel data.

I am sure there are several options to do this (quite basic) estimation. I just don’t know which way to go, and once I decide for a specific way, how to carry it out and set it up.
I would just like to have a kind of roadmap for how to set this whole thing up.