ggplot2 Facet-Wrap Using More Than One Variable

Question

I want this ggplot-facet to look like this

set.seed(1)
n10_sd1_arma0.5_0.3 <- arima.sim(n = 10, model = list(ar = c(0.5), ma = c(0.3), order = c(1, 0, 1)), sd = 1)
set.seed(1)
n10_sd1_arma0.5_0.4 <- arima.sim(n = 10, model = list(ar = c(0.5), ma = c(0.4), order = c(1, 0, 1)), sd = 1)
set.seed(1)
n10_sd1_arma0.35_0.6 <- arima.sim(n = 10, model = list(ar = c(0.35), ma = c(0.6), order = c(1, 0, 1)), sd = 1)
set.seed(1)
n10_sd3_arma0.5_0.3 <- arima.sim(n = 10, model = list(ar = c(0.5), ma = c(0.3), order = c(1, 0, 1)), sd = 3)
set.seed(1)
n10_sd3_arma0.5_0.4 <- arima.sim(n = 10, model = list(ar = c(0.5), ma = c(0.4), order = c(1, 0, 1)), sd = 3)
set.seed(1)
n10_sd3_arma0.35_0.6 <- arima.sim(n = 10, model = list(ar = c(0.35), ma = c(0.6), order = c(1, 0, 1)), sd = 3)
set.seed(1)
n10_sd5_arma0.5_0.3 <- arima.sim(n = 10, model = list(ar = c(0.5), ma = c(0.3), order = c(1, 0, 1)), sd = 5)
set.seed(1)
n10_sd5_arma0.5_0.4 <- arima.sim(n = 10, model = list(ar = c(0.5), ma = c(0.4), order = c(1, 0, 1)), sd = 5)
set.seed(1)
n10_sd5_arma0.35_0.6 <- arima.sim(n = 10, model = list(ar = c(0.35), ma = c(0.6), order = c(1, 0, 1)), sd = 5)
set.seed(1)
n10_sd10_arma0.5_0.3 <- arima.sim(n = 10, model = list(ar = c(0.5), ma = c(0.3), order = c(1, 0, 1)), sd = 10)
set.seed(1)
n10_sd10_arma0.5_0.4 <- arima.sim(n = 10, model = list(ar = c(0.5), ma = c(0.4), order = c(1, 0, 1)), sd = 10)
set.seed(1)
n10_sd10_arma0.35_0.6 <- arima.sim(n = 10, model = list(ar = c(0.35), ma = c(0.6), order = c(1, 0, 1)), sd = 10)

xx = 1:10

n10_df <- data.frame(xx = 1:10, x1 = n10_sd1_arma0.5_0.3, x2 = n10_sd1_arma0.5_0.4, x3 = n10_sd1_arma0.35_0.6, x4 = n10_sd3_arma0.5_0.3, x5 = n10_sd3_arma0.5_0.4, x6 = n10_sd3_arma0.35_0.6, x7 = n10_sd5_arma0.5_0.3, x8 = n10_sd5_arma0.5_0.4, x9 = n10_sd5_arma0.35_0.6, x10 = n10_sd10_arma0.5_0.3, x11 = n10_sd10_arma0.5_0.4, x12 = n10_sd10_arma0.35_0.6)

n10_df |>
  tidyr::pivot_longer(-xx) |> 
  dplyr:: mutate(id = as.numeric(gsub("x", "", name))) |> 
  dplyr::arrange(id, xx) |> 
  dplyr::select(-id) |> 
  dplyr::mutate(sd = rep(rep(c(sd = 1, sd = 3, sd = 5, sd = 10), each = 10), each = 3),
            psi = rep(rep(list(c(0.5, 0.3), c(0.5, 0.4), c(0.35, 0.6)), each = 10), 4)) |> 
  dplyr::mutate(sd = factor(sd, levels = sd, labels = paste("sd =", sd)),
            psi = factor(psi, levels = psi, labels = gsub("c", "", paste("\U03A8 =", psi)))) |>   
  ggplot2::ggplot(aes(x = xx, y = value)) +
  ggplot2::geom_line() + 
  ggplot2::geom_point() + 
  ggplot2::scale_y_continuous(expand = c(0.0, 0.00)) +
  ggplot2::labs(x = "Time", y = "Series") +
  ggplot2::facet_grid(sd ~ psi, scales = "free_y") + 
  ggplot2::theme_bw() + ggplot2::theme(strip.text.x = ggplot2::element_text(size = 20, face = "bold"), strip.text.y = ggplot2::element_text(size = 16, face = "bold"), axis.title = ggplot2::element_text(size = 20), axis.title.x = ggplot2::element_text(angle = 0, hjust = 0.5, 

vjust = 0.5, size = 20), axis.title.y = ggplot2::element_text(angle = 90, hjust = 0.5, vjust = 0.5, size = 20))

I think my problem lies in how to twist this part rep(rep(list(c(0.5, 0.3), c(0.5, 0.4), c(0.35, 0.6)) to be what I want. Please help!

Edit

n10_df |>
  tidyr::pivot_longer(-xx) |> 
  dplyr:: mutate(id = as.numeric(gsub("x", "", name))) |> 
  dplyr::arrange(id, xx) |> 
  dplyr::select(-id) |> 
  dplyr::mutate(sd = rep(rep(c(sd = 1, sd = 3, sd = 5, sd = 10), each = 10), each = 3),
            psi = rep(rep(list(c(0.5, 0.3), c(0.5, 0.4), c(0.35, 0.6)), each = 10), 4)) |> 
  dplyr::mutate(sd = factor(sd, levels = sd, labels = paste("sd =", sd)),
            psi = factor(psi, levels = psi, labels = sapply(psi,   function(x) sprintf('\U03C6 = %s, \U1D717 = %s', x[1], x[2])))) |>   
  ggplot2::ggplot(aes(x = xx, y = value)) +
  ggplot2::geom_line() + 
  ggplot2::geom_point() + 
  ggplot2::scale_y_continuous(expand = c(0.0, 0.00)) +
  ggplot2::labs(x = "Time", y = "Series") +
  ggplot2::facet_grid(sd ~ psi, scales = "free_y") + 

ggplot2::theme_bw() + ggplot2::theme(strip.text.x = ggplot2::element_text(size = 20, face = "bold"), strip.text.y = ggplot2::element_text(size = 16, face = "bold"), axis.title = ggplot2::element_text(size = 20), axis.title.x = ggplot2::element_text(angle = 0, hjust = 0.5, vjust = 0.5, size = 20), axis.title.y = ggplot2::element_text(angle = 90, hjust = 0.5, vjust = 0.5, size = 20))